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On a superlinear elliptic boundary value problem at resonance


Author: P. J. McKenna
Journal: Proc. Amer. Math. Soc. 74 (1979), 259-265
MSC: Primary 35J65
DOI: https://doi.org/10.1090/S0002-9939-1979-0524297-1
MathSciNet review: 524297
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Abstract: Semilinear partial differential equations of the type $ - \Delta u - {\lambda _2}u + {e^u} = h$ are studied and existence and multiplicity results obtained.


References [Enhancements On Off] (What's this?)

  • [1] Lamberto Cesari, Functional analysis, nonlinear differential equations, and the alternative method, Nonlinear functional analysis and differential equations (Proc. Conf., Mich. State Univ., East Lansing, Mich., 1975) Marcel Dekker, New York, 1976, pp. 1–197. Lecture Notes in Pure and Appl. Math., Vol. 19. MR 0487630
  • [2] Svatopluk Fučík, Remarks on superlinear boundary value problems, Bull. Austral. Math. Soc. 16 (1977), no. 2, 181–188. MR 0442467, https://doi.org/10.1017/S0004972700023170
  • [3] Peter Hess, On strongly nonlinear elliptic problems, Functional analysis (Proc. Brazilian Math. Soc. Sympos., Inst. Mat. Univ. Estad. Campinas, S ao Paulo, 1974) Dekker, New York, 1976, pp. 91–109. Lecture Notes in Pure and Appl. Math., 18. MR 0602180
  • [4] L. Nirenberg, An application of generalized degree to a class of nonlinear problems, Troisième Colloque sur l’Analyse Fonctionnelle (Liège, 1970) Vander, Louvain, 1971, pp. 57–74. MR 0413207
  • [5] P. J. McKenna and J. Rauch, Strongly nonlinear perturbations of nonnegative boundary value problems with kernel, J. Differential Equations 28 (1978), no. 2, 253–265. MR 491053, https://doi.org/10.1016/0022-0396(78)90070-0
  • [6] P. J. McKenna, On the reduction of a semilinear hyperbolic problem to a Landesman-Lazer problem, Houston J. Math. 4 (1978), no. 4, 577–581. MR 523615

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1979-0524297-1
Keywords: Elliptic boundary value problem, monotone nonlinearities
Article copyright: © Copyright 1979 American Mathematical Society

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