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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 = φ 1 + φ 2 with φ 1 locally Lipschitz and φ 2 proper, convex, lower semicontinuous.

Suggested Citation

  • Michael E. Filippakis & Nikolaos S. Papageorgiou, 2004. "Solutions for nonlinear variational inequalities with a nonsmooth potential," Abstract and Applied Analysis, Hindawi, vol. 2004, pages 1-15, January.
    • Handle: RePEc:hin:jnlaaa:318012
    DOI: 10.1155/S1085337504312017
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