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Infinitely many solutions of some nonlinear variational equations. (English) Zbl 1160.49007
Summary: 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 \[ {\bar J}(u)=\int _\Omega {\bar A} (x,u)|\nabla u|^p \,dx - \int_\Omega G(x,u) \,dx \] in the Banach space \({W^{1,p}_0(\Omega) \cap L^\infty(\Omega)}\), being \(\Omega \) 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.

MSC:
49J40 Variational inequalities
35J65 Nonlinear boundary value problems for linear elliptic equations
58E05 Abstract critical point theory (Morse theory, Lyusternik-Shnirel’man theory, etc.) in infinite-dimensional spaces
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