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Solutions for nonlinear variational inequalities with a nonsmooth potential

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  • Michael E. Filippakis
  • Nikolaos S. Papageorgiou

Abstract

First we examine a resonant variational inequality driven by the p‐Laplacian and with a nonsmooth potential. We prove the existence of a nontrivial solution. Then we use this existence theorem to obtain nontrivial positive solutions for a class of resonant elliptic equations involving the p‐Laplacian and a nonsmooth potential. Our approach is variational based on the nonsmooth critical point theory for functionals of the form φ = φ1 + φ2 with φ1 locally Lipschitz and φ2 proper, convex, lower semicontinuous.

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Handle: RePEc:wly:jnlaaa:v:2004:y:2004:i:8:p:635-649
DOI: 10.1155/S1085337504312017
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