Article ID Journal Published Year Pages File Type
4609271 Journal of Differential Equations 2016 31 Pages PDF
Abstract

In this work we study the existence of nontrivial solutions for the following class of multivalued elliptic problemsequation(P)−Δu+V(x)u−ϵh(x)∈∂tF(x,u)inR2, where ϵ>0ϵ>0, V   is a continuous function verifying some conditions, h∈(H1(R2))⁎h∈(H1(R2))⁎ and ∂tF(x,u)∂tF(x,u) is the generalized gradient of F(x,t)F(x,t) with respect to t   and F(x,t)=∫0tf(x,s)ds. Assuming that f is a discontinuous function with exponential critical growth, we have applied variational methods for locally Lipschitz functional to get two solutions for (P) when ϵ is small enough.

Related Topics
Physical Sciences and Engineering Mathematics Analysis
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