Patrick Winkert

patrick_winkert Technische Universität Berlin
Institut für Mathematik
Sekretariat MA 1-0
MA 669
Straße des 17. Juni 136
10623 Berlin, Germany
+49 - 30 - 314 - 2 74 87
winkert(at)math.tu-berlin.de
Website at TU Berlin
Google Scholar
ORCID
Patrick Winkert
Curriculum Vitae

Education
  • 2015: Habilitation in Mathematics (postdoctoral qualification, Dr.rer.nat.habil.), Thesis: Global a priori bounds and multiplicity results for quasilinear elliptic equations and inequalities, Technische Universität Berlin, Berlin, Germany
  • 2009: Ph.D. in Mathematics (Dr.rer.nat.), Thesis: Comparison principles and multiple solutions for nonlinear elliptic problems, Martin-Luther-Universität Halle-Wittenberg, Halle, Germany,
  • 2006: Master in Mathematics (Diploma in Mathematics), Thesis: T-symmetrische Tensor-Differentialformen mit logarithmischen Polen, Martin-Luther-Universität Halle-Wittenberg, Halle, Germany
Employment
  • since 2019: Research Assistant (permanent), Technische Universität Berlin, Berlin, Germany
  • since 2016: Privatdozent, Technische Universität Berlin, Berlin, Germany
  • Fall 2017: Substitute Professor 'Analysis', Martin-Luther-Universität Halle-Wittenberg, Halle, Germany
  • Spring 2017: Guest Professor 'Applied Analysis', Humboldt-Universität zu Berlin, Berlin, Germany
  • Fall 2016: Substitute Professor 'Analysis', Martin-Luther-Universität Halle-Wittenberg, Halle, Germany
  • Spring 2016: Substitute Professor 'Applied Analysis', Martin-Luther-Universität Halle-Wittenberg, Halle, Germany
  • 2009 – 2019: Research Assistant, Technische Universität Berlin, Berlin, Germany
  • 2006 – 2009: Research Assistant, Martin-Luther-Universität Halle-Wittenberg, Halle, Germany
Patrick Winkert
Publications

Monographs
  1. N.S. Papageorgiou, P. Winkert, Applied Nonlinear Functional Analysis. An Introduction, Second Revised Edition, De Gruyter, Berlin, 2024, xii+722 pp. De Gruyter
  2. N.S. Papageorgiou, P. Winkert, Applied Nonlinear Functional Analysis. An Introduction, De Gruyter, Berlin, 2018, x+612 pp.
    De Gruyter
Editorials
  1. P. Candito, R. Livrea, P. Winkert, Special issue on the occasion of the 70th birthday of Professor Siegfried Carl, Nonlinear Anal. Real World Appl. 74 (2023), Paper No. 103959. Preprint   Journal   
Refereed Articles
  1. G.M. Figueiredo, M.T.O. Pimenta, P. Winkert, The asymptotic behavior of constant sign and nodal solutions of (p,q)-Laplacian problems as p goes to 1, Nonlinear Anal. 251 (2025), Paper No. 113677, 14 pp. Preprint   Journal   
  2. E. Amoroso, Á. Crespo-Blanco, P. Pucci, P. Winkert, Superlinear elliptic equations with unbalanced growth and nonlinear boundary condition, Bull. Sci. Math. 197 (2024), Paper No. 103534, 44 pp. Preprint   Journal   arXiv
  3. Á. Crespo-Blanco, L. Gasiński, P. Winkert, Least energy sign-changing solution for degenerate Kirchhoff double phase problems, J. Differential Equations 411 (2024), 51–89. Preprint   Journal   arXiv
  4. F. Vetro, P. Winkert, Logarithmic double phase problems with convection: existence and uniqueness results, Commun. Pure Appl. Anal. 23 (2024), no. 9, 1325–1339. Preprint   Journal   
  5. X. He, Y. Meng, P. Winkert, Multiple bound states for a class of fractional critical Schrödinger-Poisson systems with critical frequency, J. Math. Phys. 65 (2024), no. 7, Paper No. 071502, 23 pp. Preprint   Journal   
  6. S. Carl, P. Winkert, Parabolic double phase obstacle problems, Nonlinear Anal. Real World Appl. 80 (2024), Paper No. 104169, 14 pp. Preprint   Journal   
  7. W. Liu, G. Dai, P. Winkert, S. Zeng, Multiple positive solutions for quasilinear elliptic problems in expanding domains, Appl. Math. Optim. 90 (2024), no. 1, Paper No. 13, 23 pp. Preprint   Journal   
  8. M.M. Frisch, P. Winkert, Boundedness, existence and uniqueness results for coupled gradient dependent elliptic systems with nonlinear boundary condition, Adv. Nonlinear Anal. 13 (2024), no. 1, Paper No. 20240009, 22 pp. Preprint   Journal   
  9. F. Borer, S. Carl, P. Winkert, Elliptic p-Laplacian systems with nonlinear boundary condition, J. Math. Anal. Appl. 538 (2024), no. 2, Paper No. 128421. Preprint   Journal   arXiv
  10. E. Amoroso, G. Bonanno, G. D'Aguì, P. Winkert, Two solutions for Dirichlet double phase problems with variable exponents, Adv. Nonlinear Stud. 24 (2024), no. 3, 734–747. Preprint   Journal   
  11. H. Tao, L. Li, P. Winkert, Existence and multiplicity of solutions for fractional Schrödinger-p-Kirchhoff equations in RN, Forum Math., accepted 2024. Preprint   Journal   
  12. N.S. Papageorgiou, F. Vetro, P. Winkert, Sequences of nodal solutions for critical double phase problems with variable exponents, Z. Angew. Math. Phys. 75 (2024), no. 3, Paper No. 95. Preprint   Journal   
  13. W. Liu, G. Dai, P. Winkert, Multiple sign-changing solutions for superlinear (p,q)-equations in symmetrical expanding domains, Bull. Sci. Math. 191 (2024), Paper No. 103393, 21 pp. Preprint   Journal   
  14. E. Amoroso, A. Sciammetta, P. Winkert, Anisotropic (p,q)-Laplacian problems with superlinear nonlinearities, Commun. Anal. Mech. 16 (2024), no. 1, 1–23. Preprint   Journal   
  15. S. Zeng, V.D. Rădulescu, P. Winkert, Nonlocal double phase implicit obstacle problems with multivalued boundary conditions, SIAM J. Math. Anal. 56 (2024), no. 1, 877–912. Preprint   Journal   
  16. Á. Crespo-Blanco, P. Winkert, Nehari manifold approach for superlinear double phase problems with variable exponents, Ann. Mat. Pura Appl. (4) 203 (2024), no. 2, 605–634. Preprint   Journal   arXiv
  17. S. El Manouni, K. Perera, P. Winkert, (p,q)-Laplacian problems with parameters in bounded and unbounded domains, Houston J. Math. 49 (2023), no. 4, 921–937. Preprint   Journal   
  18. N.S. Papageorgiou, F. Vetro, P. Winkert, Sign changing solutions for critical double phase problems with variable exponent, Z. Anal. Anwend. 42 (2023), no. 1-2, 235–251. Preprint   Journal   
  19. K. Ho, P. Winkert, New embedding results for double phase problems with variable exponents and a priori bounds for corresponding generalized double phase problems, Calc. Var. Partial Differential Equations 62 (2023), no. 8, Paper No. 227, 38 pp. Preprint   Journal   arXiv
  20. K. Ho, P. Winkert, Infinitely many solutions to Kirchhoff double phase problems with variable exponents, Appl. Math. Lett. 145 (2023), Paper No. 108783, 8 pp. Preprint   Journal   arXiv
  21. H. Tao, L. Li, P. Winkert, Existence and concentration of solutions for a 1-biharmonic Choquard equation with steep potential well in RN, J. Geom. Anal. 33 (2023), no. 9, Paper No. 276, 27 pp. Preprint   Journal   
  22. F. Vetro, P. Winkert, Nodal solutions for critical Robin double phase problems with variable exponent, Discrete Contin. Dyn. Syst. Ser. S 16 (2023), no. 11, 3333–3349. Preprint   Journal   
  23. R. Arora, A. Fiscella, T. Mukherjee, P. Winkert, Existence of ground state solutions for a Choquard double phase problem, Nonlinear Anal. Real World Appl. 73 (2023), Paper No. 103914, 22 pp. Preprint   Journal   arXiv
  24. Y. Yang, W. Liu, P. Winkert, X. Yan, Existence of solutions for resonant double phase problems with mixed boundary value conditions, Partial Differ. Equ. Appl. 4 (2023), no. 3, Paper No. 18, 17 pp. Preprint   Journal   
  25. S. Zeng, Y. Bai, V.D. Rădulescu, P. Winkert, An inverse problem for a double phase implicit obstacle problem with multivalued terms, ESAIM Control Optim. Calc. Var. 29 (2023), Paper No. 30, 23 pp. Preprint   Journal   
  26. U. Guarnotta, R. Livrea, P. Winkert, The sub-supersolution method for variable exponent double phase systems with nonlinear boundary conditions, Atti Accad. Naz. Lincei Rend. Lincei Mat. Appl. 34 (2023), no. 3, 617–639. Preprint   Journal   arXiv
  27. R. Arora, A. Fiscella, T. Mukherjee, P. Winkert, On double phase Kirchhoff problems with singular nonlinearity, Adv. Nonlinear Anal. 12 (2023), no. 1, Paper No. 20220312, 24 pp. Preprint   Journal   arXiv
  28. Y. Liu, V.T. Nguyen, P. Winkert, S. Zeng, Coupled double phase obstacle systems involving nonlocal functions and multivalued convection terms, Monatsh. Math. 202 (2023), no. 2, 363–376. Preprint   Journal   
  29. A. Sciammetta, E. Tornatore, P. Winkert, Bounded weak solutions to superlinear Dirichlet double phase problems, Anal. Math. Phys. 13 (2023), no. 2, Paper No. 23, 18 pp. Preprint   Journal   
  30. S. Zeng, N.S. Papageorgiou, P. Winkert, Inverse problems for double-phase obstacle problems with variable exponents, J. Optim. Theory Appl. 196 (2023), no. 2, 666–699. Preprint   Journal   
  31. S. Zeng, L. Gasiński, V.D. Rădulescu, P. Winkert, Anisotropic and isotropic implicit obstacle problems with nonlocal terms and multivalued boundary conditions, Commun. Nonlinear Sci. Numer. Simul. 118 (2023), Paper No. 106997, 34 pp. Preprint   Journal   
  32. Á. Crespo-Blanco, N.S. Papageorgiou, P. Winkert, (p,q)-Equations with negative concave terms, J. Geom. Anal. 33 (2023), no. 1, Paper No. 5, 26 pp. Preprint   Journal   
  33. F. Vetro, P. Winkert, Constant sign solutions for double phase problems with variable exponents, Appl. Math. Lett. 135 (2023), Paper No. 108404, 7 pp. Preprint   Journal   
  34. G. D'Aguì, A. Sciammetta, P. Winkert, On the Fučík spectrum of the p-Laplacian with no-flux boundary condition, Nonlinear Anal. Real World Appl. 69 (2023) 103736, 17 pp. Preprint   Journal   
  35. G. D'Aguì, A. Sciammetta, E. Tornatore, P. Winkert, Parametric Robin double phase problems with critical growth on the boundary, Discrete Contin. Dyn. Syst. Ser. S 16 (2023), no. 6, 1286–1299. Preprint   Journal   
  36. S. Zeng, V.D. Rădulescu, P. Winkert, Double phase obstacle problems with multivalued convection and mixed boundary value conditions, Discrete Contin. Dyn. Syst. Ser. B 28 (2023), no. 2, 999–1023. Preprint   Journal   arXiv
  37. S. Zeng, Y. Bai, P. Winkert, J.-C. Yao, Identification of discontinuous parameters in double phase obstacle problems, Adv. Nonlinear Anal. 12 (2023), no. 1, 1–22. Preprint   Journal   
  38. C. Farkas, A. Fiscella, P. Winkert, On a class of critical double phase problems, J. Math. Anal. Appl. 515 (2022), no. 2, 126420, 16 pp. Preprint   Journal   arXiv
  39. F. Vetro, P. Winkert, Existence, uniqueness and asymptotic behavior of parametric anisotropic (p,q)-equations with convection, Appl. Math. Optim. 86 (2022), no. 2, Paper No. 18, 18 pp. Preprint   Journal   
  40. R. Arora, A. Fiscella, T. Mukherjee, P. Winkert, On critical double phase Kirchhoff problems with singular nonlinearity, Rend. Circ. Mat. Palermo (2) 71 (2022), no. 3, 1079–1106. Preprint   Journal   
  41. S. Zeng, V.D. Rădulescu, P. Winkert, Double phase obstacle problems with variable exponent, Adv. Differential Equations 27 (2022), no. 9-10, 611–645. Preprint   Journal   
  42. W. Liu, G. Dai, N.S. Papageorgiou, P. Winkert, Existence of solutions for singular double phase problems via the Nehari manifold method, Anal. Math. Phys. 12 (2022), no. 3, Paper No. 75, 25 pp. Preprint   Journal   arXiv
  43. Á. Crespo-Blanco, L. Gasiński, P. Harjulehto, P. Winkert, A new class of double phase variable exponent problems: Existence and uniqueness, J. Differential Equations 323 (2022), 182–228. Preprint   Journal   arXiv
  44. K. Ho, Y.-H. Kim, P. Winkert, C. Zhang, The boundedness and Hölder continuity of solutions to elliptic equations involving variable exponents and critical growth, J. Differential Equations 313 (2022), 503–532. Preprint   Journal   arXiv
  45. S. Zeng, V.D. Rădulescu, P. Winkert, Double phase implicit obstacle problems with convection and multivalued mixed boundary value conditions, SIAM J. Math. Anal. 54 (2022), no. 2, 1898–1926. Preprint   Journal   arXiv
  46. W. Liu, P. Winkert, Combined effects of singular and superlinear nonlinearities in singular double phase problems in RN, J. Math. Anal. Appl. 507 (2022), no. 2, 125762, 19 pp. Preprint   Journal   arXiv
  47. Á. Crespo-Blanco, N.S. Papageorgiou, P. Winkert, Parametric superlinear double phase problems with singular term and critical growth on the boundary, Math. Methods Appl. Sci. 45 (2022), no. 4, 2276–2298. Preprint   Journal   arXiv
  48. N.S. Papageorgiou, P. Winkert, A multiplicity theorem for anisotropic Robin equations, Atti Accad. Naz. Lincei Rend. Lincei Mat. Appl. 33 (2022), no. 1, 1–22. Preprint   Journal   arXiv
  49. S. El Manouni, G. Marino, P. Winkert, Existence results for double phase problems depending on Robin and Steklov eigenvalues for the p-Laplacian, Adv. Nonlinear Anal. 11 (2022), no. 1, 304–320. Preprint   Journal   arXiv
  50. N.S. Papageorgiou, P. Winkert, On a class of singular anisotropic (p,q)-equations, Rev. Mat. Complut. 35 (2022), no. 2, 545–571. Preprint   Journal   arXiv
  51. C. Farkas, A. Fiscella, P. Winkert, Singular Finsler double phase problems with nonlinear boundary condition, Adv. Nonlinear Stud. 21 (2021), no. 4, 809–825. Preprint   Journal   arXiv
  52. N.S. Papageorgiou, P. Winkert, Existence and nonexistence of positive solutions for singular (p,q)-equations with superdiffusive perturbation, Results Math. 76 (2021), no. 4, Paper No. 169, 20 pp. Preprint   Journal   arXiv
  53. N.S. Papageorgiou, P. Winkert, Positive solutions for singular anisotropic (p,q)-equations, J. Geom. Anal. 31 (2021), no. 12, 11849–11877. Preprint   Journal   arXiv
  54. C. Farkas, P. Winkert, An existence result for singular Finsler double phase problems, J. Differential Equations 286 (2021), 455–473. Preprint   Journal   arXiv
  55. L. Gasiński, P. Winkert, Sign changing solution for a double phase problem with nonlinear boundary condition via the Nehari manifold, J. Differential Equations 274 (2021), 1037–1066. Preprint   Journal   arXiv
  56. N.S. Papageorgiou, P. Winkert, Singular Dirichlet (p,q)-equations, Mediterr. J. Math. 18 (2021), no. 4, Paper No. 141, 20 pp. Preprint   Journal   arXiv
  57. S. Zeng, Y. Bai, L. Gasiński, P. Winkert, Convergence analysis for double phase obstacle problems with multivalued convection term, Adv. Nonlinear Anal. 10 (2021), no. 1, 659–672. Preprint   Journal   
  58. A. Bahrouni, V.D. Rădulescu, P. Winkert, Small perturbations of Robin problems driven by the p-Laplacian plus a positive potential, Topol. Methods Nonlinear Anal. 57 (2021), no. 2, 663–673. Preprint   Journal   
  59. N.S. Papageorgiou, P. Winkert, (p,q)-Equations with singular and concave convex nonlinearities, Appl. Math. Optim. 84 (2021), no. 3, 2601–2628. Preprint   Journal   arXiv
  60. S. Zeng, L. Gasiński, P. Winkert, Y. Bai, Existence of solutions for double phase obstacle problems with multivalued convection term, J. Math. Anal. Appl. 501 (2021), no. 1, 123997, 12 pp. Preprint   Journal   
  61. N.S. Papageorgiou, P. Winkert, Positive solutions for weighted singular p-Laplace equations via Nehari manifolds, Appl. Anal. 100 (2021), no. 11, 2436–2448. Preprint   Journal   arXiv
  62. A. Bahrouni, V.D. Rădulescu, P. Winkert, Double phase problems with variable growth and convection for the Baouendi-Grushin operator, Z. Angew. Math. Phys. 71 (2020), no. 6, 183. Preprint   Journal   
  63. A. Bahrouni, V.D. Rădulescu, P. Winkert, Robin fractional problems with symmetric variable growth, J. Math. Phys. 61 (2020), no. 10, 101503, 14 pp. Preprint   Journal   arXiv
  64. S. Zeng, Y. Bai, L. Gasiński, P. Winkert, Existence results for double phase implicit obstacle problems involving multivalued operators, Calc. Var. Partial Differential Equations 59 (2020), no. 5, Paper No. 176, 18 pp. Preprint   Journal   
  65. G. Marino, P. Winkert, Existence and uniqueness of elliptic systems with double phase operators and convection terms, J. Math. Anal. Appl. 492 (2020), no. 1, 124423, 13 pp. Preprint   Journal   arXiv
  66. A. Bahrouni, V.D. Rădulescu, P. Winkert, A critical point theorem for perturbed functionals and low perturbations of differential and nonlocal systems, Adv. Nonlinear Stud. 20 (2020), no. 3, 663–674. Preprint   Journal   
  67. G. Marino, P. Winkert, L-bounds for general singular elliptic equations with convection term, Appl. Math. Lett. 107 (2020), 106410, 6 pp. Preprint   Journal   arXiv
  68. L. Gasiński, P. Winkert, Constant sign solutions for double phase problems with superlinear nonlinearity, Nonlinear Anal. 195 (2020), 111739, 9 pp. Preprint   Journal   arXiv
  69. Y. Bai, L. Gasiński, P. Winkert, S. Zeng, W1,p versus C1: The nonsmooth case involving critical growth, Bull. Math. Sci. 10 (2020), no. 3, 2050009, 15 pp. Preprint   Journal   
  70. L. Gasiński, P. Winkert, Existence and uniqueness results for double phase problems with convection term, J. Differential Equations 268 (2020), no. 8, 4183–4193. Preprint   Journal   arXiv
  71. G. Marino, P. Winkert, Global a priori bounds for weak solutions of quasilinear elliptic systems with nonlinear boundary condition, J. Math. Anal. Appl. 482 (2020), no. 2, 123555, 19 pp. Preprint   Journal   arXiv
  72. S.A. Marano, P. Winkert, Corrigendum to ''On a quasilinear elliptic problem with convection term and nonlinear boundary condition'' [Nonlinear Anal. 187 (2019), 159–169], Nonlinear Anal. 189 (2019), 111578. Preprint   Journal   
  73. G. D'Aguì, B. Di Bella, P. Winkert, Two positive solutions for nonlinear fourth-order elastic beam equations, Electron. J. Qual. Theory Differ. Equ. 2019, Paper No. 37, 12 pp. Preprint   Journal   
  74. G. Bonanno, G. D'Aguì, P. Winkert, A two critical points theorem for non-differentiable functions and applications to highly discontinuous PDE's, Pure Appl. Funct. Anal. 4 (2019), no. 4, 709–725. Preprint   Journal   
  75. S.A. Marano, P. Winkert, On a quasilinear elliptic problem with convection term and nonlinear boundary condition, Nonlinear Anal. 187 (2019), 159–169. Preprint   Journal   
  76. D. Motreanu, P. Winkert, Existence and asymptotic properties for quasilinear elliptic equations with gradient dependence, Appl. Math. Lett. 95 (2019), 78–84. Preprint   Journal   
  77. N.S. Papageorgiou, P. Winkert, Nonlinear systems with Hartman-type perturbations, Monatsh. Math. 190 (2019), no. 2, 389–404. Preprint   Journal   
  78. G. Marino, P. Winkert, Moser iteration applied to elliptic equations with critical growth on the boundary, Nonlinear Anal. 180 (2019), 154–169. Preprint   Journal   arXiv
  79. N.S. Papageorgiou, P. Winkert, Solutions with sign information for nonlinear nonhomogeneous problems, Math. Nachr. 292 (2019), no. 4, 871–891. Preprint   Journal   
  80. N.S. Papageorgiou, P. Winkert, Singular p-Laplacian equations with superlinear perturbation, J. Differential Equations 266 (2019), no. 2-3, 1462–1487. Preprint   Journal   
  81. N.S. Papageorgiou, P. Winkert, Double resonance for Robin problems with indefinite and unbounded potential, Discrete Contin. Dyn. Syst. Ser. S 11, (2018), no. 2, 323–344. Preprint   Journal   
  82. N.S. Papageorgiou, P. Winkert, Asymmetric (p,2)-equations, superlinear at +∞, resonant at -∞, Bull. Sci. Math. 141 (2017), no. 5, 443–488. Preprint   Journal   
  83. S. El Manouni, H. Hajaiej, P. Winkert, Bounded solutions to nonlinear problems in RN involving the fractional Laplacian depending on parameters, Minimax Theory Appl. 2 (2017), no. 2, 265–283. Preprint   Journal   arXiv
  84. N.S. Papageorgiou, P. Winkert, Positive solutions for nonlinear nonhomogeneous Dirichlet problems with concave-convex nonlinearities, Positivity 20 (2016), no. 4, 945–979. Preprint   Journal   
  85. P. Winkert, R. Zacher, Global a priori bounds for weak solutions to quasilinear parabolic equations with nonstandard growth, Nonlinear Anal. 145 (2016), 1–23. Preprint   Journal   arXiv
  86. N.S. Papageorgiou, P. Winkert, Nonlinear Robin problems with a reaction of arbitrary growth, Ann. Mat. Pura Appl. (4) 195 (2016), no. 4, 1207–1235. Preprint   Journal   
  87. G. Bonanno, G. D'Aguì, P. Winkert, Sturm-Liouville equations involving discontinuous nonlinearities, Minimax Theory Appl. 1 (2016), no. 1, 125–143. Preprint   Journal   
  88. N.S. Papageorgiou, P. Winkert, Nonlinear nonhomogeneous Dirichlet equations with a superlinear nonlinearity, Results Math. 70 (2016), no. 1, 31–79. Preprint   Journal   arXiv
  89. P. Winkert, R. Zacher, Corrigendum to ''A priori bounds for weak solutions to elliptic equations with nonstandard growth'' [Discrete Contin. Dyn. Syst. Ser. S 5 (2012), 865–878], Discrete Contin. Dyn. Syst. Ser. S, published on-line as note, 2015, 1–3. Preprint   Journal   arXiv
  90. S. El Manouni, N.S. Papageorgiou, P. Winkert, Parametric nonlinear nonhomogeneous Neumann equations involving a nonhomogeneous differential operator, Monatsh. Math. 177 (2015), no. 2, 203–233. Preprint   Journal   
  91. N.S. Papageorgiou, P. Winkert, Resonant (p,2)-equations with concave terms, Appl. Anal. 94 (2015), no. 2, 342–360. Preprint   Journal   
  92. P. Winkert, On the boundedness of solutions to elliptic variational inequalities, Set-Valued Var. Anal. 22 (2014), no. 4, 763–781. Preprint   Journal   
  93. G. Bonanno, P. Winkert, Multiplicity results to a class of variational-hemivariational inequalities, Topol. Methods Nonlinear Anal. 43 (2014), no. 2, 493–516. Preprint   Journal   
  94. N.S. Papageorgiou, P. Winkert, On a parametric nonlinear Dirichlet problem with subdiffusive and equidiffusive reaction, Adv. Nonlinear Stud. 14 (2014), no. 3, 747–773. Preprint   Journal   
  95. G. Bonanno, D. Motreanu, P. Winkert, Boundary value problems with nonsmooth potential, constraints and parameters, Dynam. Systems Appl. 22 (2013), no. 2-3, 385–396. Preprint   Journal   
  96. P. Winkert, Multiplicity results for a class of elliptic problems with nonlinear boundary condition, Commun. Pure Appl. Anal. 12 (2013), no. 2, 785–802. Preprint   Journal   
  97. P. Winkert, R. Zacher, A priori bounds for weak solutions to elliptic equations with nonstandard growth, Discrete Contin. Dyn. Syst. Ser. S 5 (2012), no. 4, 865–878. Preprint   Journal   arXiv
  98. D. Motreanu, P. Winkert, On the Fučík spectrum for the p-Laplacian with Robin boundary condition, Nonlinear Anal. 74 (2011), no. 14, 4671–4681. Preprint   Journal   
  99. G. Bonanno, D. Motreanu, P. Winkert, Variational-hemivariational inequalities with small perturbations of nonhomogeneous Neumann boundary conditions, J. Math. Anal. Appl. 381 (2011), no. 2, 627–637. Preprint   Journal   
  100. P. Winkert, Multiple solution results for elliptic Neumann problems involving set-valued nonlinearities, J. Math. Anal. Appl. 377 (2011), no. 1, 121–134. Preprint   Journal   
  101. D. Motreanu, P. Winkert, Variational-hemivariational inequalities with nonhomogeneous Neumann boundary condition, Matematiche (Catania) 65 (2010), no. 2, 109–119. Preprint   Journal   
  102. P. Winkert, Sign-changing and extremal constant-sign solutions of nonlinear elliptic Neumann boundary value problems, Bound. Value Probl. 2010, Art. ID 139126, 22 pp. Preprint   Journal   
  103. P. Winkert, Local C1-minimizers versus local W1,p-minimizers of nonsmooth functionals, Nonlinear Anal. 72 (2010), no. 11, 4298–4303. Preprint   Journal   
  104. P. Winkert, L-estimates for nonlinear elliptic Neumann boundary value problems, NoDEA Nonlinear Differential Equations Appl. 17 (2010), no. 3, 289–302. Preprint   Journal   
  105. P. Winkert, Constant-sign and sign-changing solutions for nonlinear elliptic equations with Neumann boundary values, Adv. Differential Equations 15 (2010), no. 5-6, 561–599. Preprint   Journal   
  106. P. Winkert, Entire extremal solutions for elliptic inclusions of Clarke′s gradient type, Z. Anal. Anwend. 29 (2010), no. 1, 63–75. Preprint   Journal   
  107. S. Carl, P. Winkert, General comparison principle for variational-hemivariational inequalities, J. Inequal. Appl. 2009, Art. ID 184348, 29 pp. Preprint   Journal   
  108. P. Brückmann, P. Winkert, T-symmetrical tensor differential forms with logarithmic poles along a hypersurface section, Int. J. Pure Appl. Math. 46 (2008), no. 1, 111–136. Preprint   Journal   
  109. P. Winkert, Discontinuous variational-hemivariational inequalities involving the p-Laplacian, J. Inequal. Appl. 2007, Art. ID 13579, 11 pp. Preprint   Journal   
Book Contributions
  1. D. Motreanu, P. Winkert, Elliptic problems with nonhomogeneous differential operators and multiple solutions, Chapter 15 in: Mathematics Without Boundaries (Surveys in Pure Mathematics), 357–379, Springer, New York, 2014. PDF   Book chapter
  2. D. Motreanu, P. Winkert, The Fucik spectrum for the negative p-Laplacian with different boundary conditions, Chapter 28 in: Nonlinear Analysis (Stability, Approximation, and Inequalities), 471–485, Springer, New York, 2012. PDF   Book chapter
Theses
  1. P. Winkert, Global a priori bounds and multiplicity results for quasilinear elliptic equations and inequalities, Habilitation thesis, Technische Universität Berlin, Berlin, Germany, November 2015. PDF
  2. P. Winkert, Comparison principles and multiple solutions for nonlinear elliptic problems, PhD thesis, Martin-Luther-Universität Halle-Wittenberg, Halle, Germany, July 2009. PDF
  3. P. Winkert, T-symmetrische Tensor-Differentialformen mit logarithmischen Polen, Diploma thesis, Martin-Luther-Universität Halle-Wittenberg, Halle, Germany, July 2006 (available only in German).
Patrick Winkert
Teaching

Teaching Experience
  • Fall 2024
    • Lectures 'Analysis I und Lineare Algebra für Ingenieurwissenschaften'
  • Spring 2024
    • Lectures 'Analysis I und Lineare Algebra für Ingenieurwissenschaften'
    • Lectures 'Analysis II für Ingenieurwissenschaften'
  • Fall 2023
    • Lectures 'Analysis II für Ingenieurwissenschaften'
  • Spring 2023
    • Lectures 'Analysis I und Lineare Algebra für Ingenieurwissenschaften'
    • Lectures 'Analysis II für Ingenieurwissenschaften'
  • Fall 2022
    • Lectures 'Analysis III für Mathematikerinnen und Mathematiker'
    • Lectures 'Analysis I und Lineare Algebra für Ingenieurwissenschaften'
  • Spring 2022
    • Lectures 'Analysis II für Mathematikerinnen und Mathematiker'
  • Fall 2021
    • Lectures 'Analysis I für Mathematikerinnen und Mathematiker'
    • Lectures 'Analysis I und Lineare Algebra für Ingenieurwissenschaften'
  • Spring 2021
    • Lectures 'Analysis I und Lineare Algebra für Ingenieurwissenschaften'
    • Lectures 'Analysis II für Ingenieurwissenschaften'
    • Seminar 'Differentialgleichungen' (with E. Emmrich)
  • Fall 2020
    • Lectures 'Analysis I und Lineare Algebra für Ingenieurwissenschaften'
  • Spring 2020
    • Lectures 'Lineare Algebra für Ingenieurwissenschaften'
    • Lectures 'Analysis I und Lineare Algebra für Ingenieurwissenschaften'
    • Seminar 'Differentialgleichungen' (with H.-C. Kreusler)
  • Fall 2019
    • Lectures 'Analysis I für Ingenieurwissenschaften'
    • Lectures 'Analysis I und Lineare Algebra für Ingenieurwissenschaften'
  • Spring 2019
    • Lectures 'Analysis I für Ingenieurwissenschaften'
    • Tutorials 'Lineare Algebra für Ingenieurwissenschaften'
    • Seminar 'Differentialgleichungen' (with H.-C. Kreusler and R. Kruse)
  • Fall 2018
    • Lectures 'Analysis I für Ingenieurwissenschaften'
    • Tutorials 'Lineare Algebra für Ingenieurwissenschaften'
  • Spring 2018
    • Lectures 'Lineare Algebra für Ingenieurwissenschaften'
    • Tutorials 'Lineare Algebra für Ingenieurwissenschaften'
  • Fall 2017
    • Lectures 'Funktionalanalysis' (MLU Halle)
    • Lectures 'Partielle Differentialgleichungen' (MLU Halle)
    • Lectures 'Lineare Algebra für Ingenieurwissenschaften'
  • Spring 2017
    • Lectures 'Lineare Algebra und Analytische Geometrie II' (HU Berlin)
    • Tutorials 'Lineare Algebra und Analytische Geometrie II' (HU Berlin)
  • Fall 2016
    • Lectures 'Funktionalanalysis' (MLU Halle)
    • Lectures 'Dynamische Systeme' (MLU Halle)
    • Tutorials 'Dynamische Systeme' (MLU Halle)
    • Seminar 'Fachseminar Analysis' (with S. Carl, MLU Halle)
    • Lectures 'Lineare Algebra für Ingenieurwissenschaften'
  • Spring 2016
    • Lectures 'Maßtheorie' (MLU Halle)
    • Lectures 'Partielle Differentialgleichungen' (MLU Halle)
  • Fall 2015
    • Lectures 'Lineare Algebra für Ingenieurwissenschaften'
    • Tutorials 'Lineare Algebra für Ingenieurwissenschaften'
  • Spring 2015
    • Tutorials 'Lineare Algebra für Ingenieurwissenschaften'
  • Fall 2014
    • Tutorials 'Analysis I für Ingenieurwissenschaften'
  • Spring 2014
    • Tutorials 'Lineare Algebra für Ingenieurwissenschaften'
  • Fall 2013
    • Tutorials 'Lineare Algebra für Ingenieurwissenschaften'
  • Spring 2013
    • Tutorials 'Lineare Algebra für Ingenieurwissenschaften'
  • Fall 2011
    • Lectures 'Funktionalanalysis II'
  • Spring 2011
    • Lectures 'Funktionalanalysis I'
    Fall 2008
    • Tutorials 'Analysis I' (MLU Halle)
Patrick Winkert
Research

Research Interests
  • A priori bounds for elliptic and parabolic problems (equations and inequalities)
  • Comparison principles and multiple solutions for nonlinear elliptic problems
  • Isotropic and anisotropic double phase problems
  • Fucik spectrum of elliptic operators
  • Gradient dependence on the right-hand side (convection term)
  • Morse theory and critical groups
  • Nonhomogeneous operators
  • Nonlinear elliptic and parabolic differential equations and inclusion
  • Nonsmooth variational problems (variational- and hemivariational inequalities)
  • Singular problems
Patrick Winkert
Editorial Activities

Member of the Editorial Board of the following journals:
Guest Editor:
Patrick Winkert
Supervision

Supervised PhD ThesesSupervised Master Theses
  1. Singular double phase Kirchhoff problems with nonlinear Neumann boundary condition, TU Berlin, August 2024.
  2. Existence results for double phase problems via the Nehari manifold, TU Berlin, July 2021.
  3. Constant-sign and sign-changing solutions for nonlinear elliptic equations, TU Berlin, December 2020.
  4. Existenz von Lösungen für quasilineare elliptische Gleichungen mit gradientenabhängigen rechten Seiten, TU Berlin, June 2019.
  5. Lösbarkeit von Variations-Hemivariationsungleichungen mit Hilfe von Ober- und Unterlösung, TU Berlin, April 2016.
Supervised Bachelor Theses
  1. Existenz und Eindeutigkeit für quasilineare elliptische Systeme mit gekoppelten gradientenabhängigen rechten Seiten, TU Berlin, April 2023.
  2. Existenz von Lösungen bei Double-Phase-Problemen mittels kritischer Punkttheorie, TU Berlin, September 2021.
  3. Die Theorie des Bochner-Integrals, TU Berlin, August 2021.
  4. Die Methode von schwacher Ober- und Unterlösung für semilineare, elliptische Randwertprobleme, TU Berlin, January 2021.
  5. Die Nehari-Mannigfaltigkeit zur Lösung einer elliptischen Differentialgleichung, TU Berlin, July 2020.
  6. Der p-Laplace-Operator – Eigenschaften und Lösbarkeit zugehöriger Gleichungen, TU Berlin, January 2020.
  7. Lebesgue- und Sobolev-Räume mit variablen Exponenten, TU Berlin, September 2019.
  8. Origami: Definition in einem analytischen Kontext und Lösen spezieller Dirichlet-Probleme, MLU Halle, June 2018.
  9. Nonlinear eigenvalue problems for nonhomogeneous differential operators, MLU Halle, October 2017.
  10. Die Gelfandsche Darstellungstheorie, MLU Halle, May 2017.
  11. Das Fučík-Spektrum des p-Laplace-Operators mit Steklov-Randbedingung, TU Berlin, May 2016.
  12. De Giorgi-Iteration für quasilineare, elliptische Gleichungen mit Neumann-Randbedingung, TU Berlin, December 2015.
  13. The eigenvalue problem of the p-Laplacian with Robin boundary condition, TU Berlin, February 2013.
  14. Die Methode von Ober- und Unterlösung für nichtlineare, elliptische Gleichungen, TU Berlin, February 2013.
  15. A priori bounds for elliptic problems with nonlinear boundary condition, TU Berlin, June 2012.

Patrick Winkert
Imprint

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      Phone: +49 (0) 30 314 - 2 39 74
      Email: patrick(at)winkert.de

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