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Infinitely many solutions of some nonlinear variational equations

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Abstract

The aim of this paper is investigating the existence of one or more critical points of a family of functionals which generalizes the model problem

$$ {\bar J}(u)=\int \limits _\Omega {\bar A} (x,u)|\nabla u|^p dx - \int \limits _\Omega G(x,u) dx$$

in the Banach space \({W^{1,p}_0(\Omega) \cap L^\infty(\Omega)}\) , being Ω a bounded domain in \({\mathbb {R}^N}\) . In order to use “classical” theorems, a suitable variant of condition (C) is proved and \({W^{1,p}_0(\Omega)}\) is decomposed according to a “good” sequence of finite dimensional subspaces.

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Authors and Affiliations

  1. Dipartimento di Matematica, Università degli Studi di Bari, Via E. Orabona, 4, 70125, Bari, Italy

    Anna Maria Candela & Giuliana Palmieri

Authors
  1. Anna Maria Candela
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  2. Giuliana Palmieri
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Correspondence to Anna Maria Candela.

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The authors acknowledge the support of M.I.U.R. (research funds ex 40% and 60%).

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Candela, A.M., Palmieri, G. Infinitely many solutions of some nonlinear variational equations. Calc. Var. 34, 495–530 (2009). https://doi.org/10.1007/s00526-008-0193-2

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  • DOI: https://doi.org/10.1007/s00526-008-0193-2

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