The Ekeland variational principle for equilibrium problems revisited and applications

In this paper, we study the Ekeland variational principle for equilibrium problems under the setting of real Banach spaces. We make use of techniques related to infinite dimensional spaces to solve the weakly compact case and introduce a suitable weakened set of coerciveness to deal with the non weakly compact case. Some old results for the Euclidean space RnRn are generalized under weakened conditions of semicontinuity and applications to countable rather than finite systems of equilibrium problems on real Banach spaces are derived. Applications to quasi-hemivariational inequalities are discussed.