Hartman–Stampacchia results for stably pseudomonotone operators and non-linear hemivariational inequalities

Abstract

We are concerned with two classes of non-standard hemivariational inequalities. In the first case we establish a Hartman–Stampacchia type existence result in the framework of stably pseudomonotone operators. Next, we prove an existence result for a class of non-linear perturbations of canonical hemivariational inequalities. Our analysis includes both the cases of compact sets and of closed convex sets in Banach spaces. Applications to non-coercive hemivariational and variational–hemivariational inequalities illustrate the abstract results of this article.

Keywords:

• hemivariational inequality
• Clarke's generalized gradient
• stably pseudomonotone operator
• fixed point theorem
• set-valued mappings

AMS Subject Classifications:

• 35J85
• 47H05
• 49J53

Acknowledgements

V. Rădulescu has been supported by Grant CNCSIS PNII – 79/2007, ‘Procese Neliniare Degenerate si Singulare’.