A Variational Method for Multivalued Boundary Value Problems

Abstract

In this paper, we investigate the existence of solution for differential systems involving a $\varphi -$Laplacian operator which incorporates as a special case the well-known $p-$Laplacian operator. In this purpose, we use a variational method which relies on Szulkin’s critical point theory. We obtain the existence of solution when the corresponding Euler–Lagrange functional is coercive.