Existence results for general inequality problems with constraints (Q1811851)

The present paper is concerned with nonlinear inequality problems of the type \(F^0 (u; v-u)+h(v)-h(u) \geq 0\) for all \(v \in C\), where \(F^0\) stands for the generalized directional derivative of a locally Lipschitz functional \(F\), \(h\) is a convex, lower semicontinuous, and proper function, and \(C\) is a closed and convex subset of a Banach space \(X\). Dealing in the framework of nonsmooth critical point theory, the authors present existence results which extend different theorems of nonsmooth variational analysis. As an application, they consider variational inequalities involving the \(p\)-Laplacian operator.