Abstract

An existence theorem of systems of generalized quasivariational inclusion problems with very weak continuity and convexity assumptions is proven. From this result, recent existence theorems of other types of systems of generalized quasivariational inclusion problems with very weak continuity and convexity assumptions are established. We establish these results with a very simple and elegant method. Our results improve and generalize many recent results of these types of problems. As applications of our results, we study variants of set-valued vector Ekeland’s variational principle with weak continuity assumptions on the maps we consider, and with a simple method. Our results on set-valued or vector-valued Ekeland’s variational principle are different from known existence results of these types of problems.