Regularized equilibrium problems with application to noncoercive hemivariational inequalities. (Q703164)

Let \(K\) be a convex subset of a topological vector space. Generalizing some known results, the authors study, for a given function \(f: K \times K \rightarrow \mathbb{R},\) the following equilibrium problem: to find \(\overline{x} \in K\) such that \[ f(\overline{x},y) \geq 0 \,\,\text{for all}\,\,y \in K. \] At first, the existence result is derived under coercivity condition, without the assumption of an algebraic monotonicity of the function \(f.\) Further, the authors apply a regularization procedure for noncoercive problems and prove the existence of a solution for a topologically pseudomonotone function \(f\). Dealing with a noncoercive mixed equilibrium problem, the authors prove an existence result under a compactness-compatibility condition. As application, the existence of a solution for a noncoercive hemivariational inequality is considered.