## Existence results for general inequality problems with constraints.(English)Zbl 1031.47039

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.

### MSC:

 47J20 Variational and other types of inequalities involving nonlinear operators (general) 49J52 Nonsmooth analysis
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