The Borwein-Preiss variational principle for nonconvex countable systems of equilibrium problems

The aim of the present paper, by using the Borwein-Preiss variational principle, we prove existence results for countable systems of equilibrium problems. We establish some sufficient conditions which can guarantee two existence theorems for countable systems of equilibrium problems on closed subsets of complete metric spaces and on weakly compact subsets of real Banach spaces, respectively.