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Critical point theorems and applications to a semilinear elliptic problem

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Abstract

The objective of this article is to establish the existence of critical points for functionals of classC 2defined on real Hilbert spaces. The argument is based on the infinite dimensional Morse theory introduced by Gromoll-Meyer [13]. The abstract results are applied to study the existence of nonzero solutions for a class of semilinear elliptic problems where the nonlinearity possesses a superlinear growth on a direction of the real line.

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Authors and Affiliations

  1. Departamento de Matemática.-IMECC, Universidade Estadual de Campinas, CP 6065, 13081-970, Campinas, SP, Brazil

    E. Alves de Barros e Silva

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  1. E. Alves de Barros e Silva
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This research was partially supported by CNPq/Brazil

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de Barros e Silva, E.A. Critical point theorems and applications to a semilinear elliptic problem. NoDEA 3, 245–260 (1996). https://doi.org/10.1007/BF01195917

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  • DOI: https://doi.org/10.1007/BF01195917

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