Multivalued elliptic equation with exponential critical growth in R2R2

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.