Strongly nonlinear multivalued elliptic equations on a bounded domain

In this work we study the existence of nontrivial solution for the following class of multivalued quasilinear problems −div(φ(|∇u|)∇u)− b(u)u ∈ λ∂F (x, u) in Ω, u = 0 on ∂Ω where Ω ⊂ R is a bounded domain, N ≥ 2 and ∂F (x, u) is a generalized gradient of F (x, t) with respect to t. The main tools utilized are Variational Methods for Locally Lipschitz Functional and a Concentration Compactness Theorem for Orlicz space.