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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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On a superlinear elliptic boundary value problem at resonance
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by P. J. McKenna PDF
Proc. Amer. Math. Soc. 74 (1979), 259-265 Request permission

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
  • 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) Lecture Notes in Pure and Appl. Math., Vol. 19, Marcel Dekker, New York, 1976, pp. 1–197. MR 0487630
  • Svatopluk Fučík, Remarks on superlinear boundary value problems, Bull. Austral. Math. Soc. 16 (1977), no. 2, 181–188. MR 442467, DOI 10.1017/S0004972700023170
  • Peter Hess, On strongly nonlinear elliptic problems, Functional analysis (Proc. Brazilian Math. Soc. Sympos., Inst. Mat. Univ. Estad. Campinas, São Paulo, 1974) Lecture Notes in Pure and Appl. Math., vol. 18, Dekker, New York, 1976, pp. 91–109. MR 0602180
  • 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
  • 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, DOI 10.1016/0022-0396(78)90070-0
  • 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
  • © Copyright 1979 American Mathematical Society
  • 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