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
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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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