Existence results for nonconvex equilibrium problems

Abstract

In this paper, we establish sufficient conditions for the existence of solutions of equilibrium problems in a metric space, that do not involve any convexity assumption either for the domain or for the function. To prove these results, a weak notion of semicontinuity is considered. Furthermore, some existence results for systems of equilibrium problems are provided.

Keywords:

• equilibrium problems
• generalized semicontinuity
• coercivity conditions

AMS Subject Classification :

• 90C26
• 49J35

Acknowledgements

This work has been supported by the National Research Programme PRIN 20079PLLN7 ‘Nonlinear Optimization, Variational Inequalities, and Equilibrium Problems’.