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10 August 2004 Solutions for nonlinear variational inequalities with a nonsmooth potential
Michael E. Filippakis, Nikolaos S. Papageorgiou
Abstr. Appl. Anal. 2004(8): 635-649 (10 August 2004). DOI: 10.1155/S1085337504312017


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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Michael E. Filippakis. Nikolaos S. Papageorgiou. "Solutions for nonlinear variational inequalities with a nonsmooth potential." Abstr. Appl. Anal. 2004 (8) 635 - 649, 10 August 2004.


Published: 10 August 2004
First available in Project Euclid: 20 September 2004

zbMATH: 1133.35375
MathSciNet: MR2096944
Digital Object Identifier: 10.1155/S1085337504312017

Primary: 35J20 , 35J85

Rights: Copyright © 2004 Hindawi

Vol.2004 • No. 8 • 10 August 2004
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