Reciprocal solution existence results for a class of vector variational control inequalities with application in physics

Abstract

By considering differentiability and generalized convexity hypotheses for some functionals of multiple integral type, we propose some equivalences between the solution sets of some (weak) variational control inequalities of vector type, which depend by some uncertainty parameters, and the associated multiple objective variational control problems. Moreover, we propose the physical motivation of the problem under investigation by providing an application in the end of the paper. © 2024