On Variational Multivalued Elliptic Equations on a Bounded Domain in the Presence of Critical Growth

Abstract

We develop arguments on the critical point theory for locally Lipschitz functionals on Orlicz-Sobolev spaces, along with convexity and compactness techniques to investigate existence of solution of the multivalued equation $\displaystyle - Δ_Φ u \in \partial j(.,u) + λh \mbox{in} Ω$, where $\Omega \subset {\mathbf{R}}^N$ is a bounded smooth domain, $Φ: {\r} \longrightarrow [0,\infty)$ is a suitable N-function, ${\Delta }_{\Phi }$ is the corresponding $\Phi$-Laplacian, $\lambda >0$ is a parameter, $h:Ω\rightarrow{\r}$ is integrable and $\partial j(.,u)$ is the subdifferential of a function $j$ associated with critical growth.

arXiv comment18 pages