On well-posed isoperimetric-type constrained variational control problems

Abstract

In this paper, we investigate well-posedness and well-posedness in the generalized sense for a new class of isoperimetric-type constrained variational control problems. For this purpose, in the first part of the current paper, we introduce new versions for the concepts of monotonicity, pseudomonotonicity and hemicontinuity associated with the considered curvilinear integral functional. Thereafter, we define the approximating solution set of the considered class of isoperimetric-type constrained variational control problems. By using these completely new elements, we formulate and prove several characterization results on well-posedness and well-posedness in the generalized sense for the problem under study. Also, in order to highlight the theoretical results and tools derived in the paper, some illustrative examples are provided.