Remarks on Multivalued Variants of Ekeland Principle with Applications

This review provides an extended discussion on multivalued variants of Ekeland’s variational principle, with the aim of highlighting the importance of this special type of result. After a presentation of the background containing general problems which appear in relation to this extended and current subject, three series of results are developed to describe three multiple-valued versions of this important principle. In this part of the work, some different or improved proofs have been given, along with several special remarks from the author, together with their demonstrations. The discussion section contains an overview of many applications of such multivalued variants in solving problems issuing from real phenomena modeling.