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Positive solutions of nonpositone sublinear elliptic problems

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Języki publikacji
EN
Abstrakty
EN
Consider the problem [formula].
Rocznik
Strony
827--851
Opis fizyczny
Bibliogr. 29 poz.
Twórcy
autor
  • Universidad Nacional de Córdoba, Facultad de Matemátca, Astronimía, Física y Computación, Av. Medina Allende s.n., Ciudad Universitaria, Córdoba, Argentina
Bibliografia
  • [1] A. Ambrosetti, D. Arcoya, B. Buffoni, Positive solutions for some semi-positone problems via bifurcation theory, Differential Integral Equations 7 (1994), no. 3–4, 655–663.
  • [2] I.M. Bachar, H. Mâagli, H. Eltayeb, Nonnegative solutions for a class of semipositone nonlinear elliptic equations in bounded domains of Rn, Opuscula Math. 42 (2022), no. 6, 793–803.
  • [3] H. Berestycki, I. Capuzzo Dolcetta, L. Nirenberg, Superlinear indefinite elliptic problems and nonlinear Liouville theorems, Topol. Methods Nonlinear Anal. 4 (1994), no. 1, 59–78.
  • [4] A. Cannas da Silva, Lectures on Symplectic Geometry, Lecture Notes in Math., vol. 1764, Springer-Verlag, Berlin, 2001.
  • [5] A. Castro, R. Shivaji, Nonnegative solutions for a class of nonpositone problems, Proc. Roy. Soc. Edinburgh Sect. A. 108 (1988), no. 3–4, 291–302.
  • [6] A. Castro, R. Shivaji, Non-negative solutions for a class of radially symmetric non-positive problems, Proc. Amer. Math. Soc. 106 (1989), no. 3, 735–740.
  • [7] A. Castro, J.B. Garner, R. Shivaji, Existence results for classes of sublinear semipositone problems, Results Math. 23 (1993), no. 3–4, 214–220.
  • [8] A. Castro, C. Maya, R. Shivaji, Nonlinear eigenvalue problems with semipositone structure, Electron. J. Differential Equations 5 (2000), 33–49.
  • [9] D.G. Costa, H. Ramos Quoirin, H. Therani, A variational approach to superlinear semipositone elliptic problems, Proc. Amer. Math. Soc. 145 (2017), no. 6, 2661–2675.
  • [10] D.G. Costa, H. Tehrani, J. Yang, On a variational approach to existence and multiplicity results for semipositone problems, Electron. J. Differential Equations 2006 (2006), no. 11, 1–10.
  • [11] E.N. Dancer, J. Shi, Uniqueness and nonexistence of positive solutions to semipositone problems, Bull. Lond. Math. Soc. 38 (2006), no. 6, 1033–1044.
  • [12] D.G. De Figueiredo, Positive solutions of semilinear elliptic equations, [in:] Differential Equations, Lecture Notes in Math., vol. 957, 1982, 34–87.
  • [13] J. Garcia-Melian, I. Iturriaga, H. Ramos Quoirin, A priori bounds and existence of solutions for slightly superlinear elliptic problems, Adv. Nonlinear Stud. 15 (2015), no. 4, 923–938.
  • [14] B. Gidas, J. Spruck, A priori bounds for positive solutions of nonlinear elliptic equations, Comm. Partial Differential Equations 6 (1981), no. 8, 883–901.
  • [15] T. Godoy, J.P. Gossez, S. Paczka, A minimax formula for the principal eigenvalues of Dirichlet problems and its applications, Electron. J. Differential Equations 16 (2007), 137–154.
  • [16] D. Gilbarg, N.S. Trudinger, Elliptic Partial Differential Equations of Second Order, Springer-Verlag, Berlin–Heidelberg–New York, 2001.
  • [17] M.W. Hirsch, Differential Topology, Graduate Texts in Mathematics, vol. 33, Springer-Verlag, New York–Heidelberg, 1976.
  • [18] U. Kaufmann, H. Ramos Quoirin, Positive solutions of indefinite semipositone problems via sub-super solutions, Differential Integral Equations 31 (2018), no. 7–8, 497–506.
  • [19] U. Kaufmann, H. Ramos Quoirin, K. Umezu, Uniqueness and sign properties of minimizers in a quasilinear indefinite problem, Commun. Pure Appl. Anal. 20 (2021), no. 6, 2313–2322.
  • [20] J.M. Lee, Introduction to Smooth Manifolds, Graduate Texts in Mathematics, vol. 218, Springer-Verlag, New York, 2003.
  • [21] E. Lee, R. Shivaji, J. Ye, Subsolutions: a journey from positone to infinite semipositone problems, Electron. J. Differential Equations 17 (2009), 123–131.
  • [22] R. Ma, Y. Zhang, Y. Zhu, Positive solutions of indefinite semipositone elliptic problems, Qual. Theory Dyn. Syst. 23 (2024), Paper no. 45.
  • [23] J. Mawhin, Leray–Schauder degree: a half century of extensions and applications, Topol. Methods Nonlinear Anal. 14 (1999), no. 2, 195–228.
  • [24] N.S. Papageorgiou, V.D. Rădulescu, D.D. Repovš, Nonlinear Analysis – Theory and Methods, Springer Monographs in Mathematics, Springer, Cham, 2019.
  • [25] A. Rhazani, G.M. Figueiredo, Positive solutions for a semipositone anisotropic p-Laplacian problem, Bound. Value Probl. 2024 (2024), Paper no. 34.
  • [26] W. Rudin, Functional Analysis, 2nd ed., International Series in Pure and Applied Mathematics, McGraw-Hill, Inc., New York, 1991.
  • [27] J.C. Sabina de Lis, Hopf maximum principle revisited, Electron. J. Differential Equations 2015 (2015), no. 115, 1–9.
  • [28] A. Santos, C.O. Alves, E. Massa, A nonsmooth variational approach to semipositone quasilinear problems in RN, J. Math. Anal. Appl. 527 (2023), 127432.
  • [29] E. Zeidler, Nonlinear Functional Analysis and its Applications, Volume 1, Springer-Verlag, New York, 1985.
Uwagi
Opracowanie rekordu ze środków MEiN, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2022-2023)
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-13aadd4e-6f0a-4aa5-80dc-094b4002b338
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