## Abstract and Applied Analysis

### Existence results for general inequality problems with constraints

#### Abstract

This paper is concerned with existence results for inequality problems of type $F^{0}(u;v)+\Psi'(u;v)\geq 0$, for all $v\in X$, where $X$ is a Banach space, $F:X\rightarrow\mathbb{R}$ is locally Lipschitz, and $\Psi:X\rightarrow(- \infty+\infty]$ is proper, convex, and lower semicontinuous. Here $F^0$ stands for the generalized directional derivative of $F$ and $\Psi'$ denotes the directional derivative of $\Psi$. The applications we consider focus on the variational-hemivariational inequalities involving the $p$-Laplacian operator.

#### Article information

Source
Abstr. Appl. Anal., Volume 2003, Number 10 (2003), 601-619.

Dates
First available in Project Euclid: 1 June 2003

https://projecteuclid.org/euclid.aaa/1054513099

Digital Object Identifier
doi:10.1155/S1085337503210058

Mathematical Reviews number (MathSciNet)
MR1990855

Zentralblatt MATH identifier
1031.47039

#### Citation

Dincă, George; Jebelean, Petru; Motreanu, Dumitru. Existence results for general inequality problems with constraints. Abstr. Appl. Anal. 2003 (2003), no. 10, 601--619. doi:10.1155/S1085337503210058. https://projecteuclid.org/euclid.aaa/1054513099