Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

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



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
MathSciNet review: 524297
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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
  • [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, 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

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 35J65

Retrieve articles in all journals with MSC: 35J65

Additional Information

Keywords: Elliptic boundary value problem, monotone nonlinearities
Article copyright: © Copyright 1979 American Mathematical Society