Multi-Valued Variational Equations

The aim of this chapter is to become acquainted with multi-valued pseudomonotone operators and to prove existence and enclosure results for the above multi-valued equations based on a straightforward extension of the notion of sub-supersolutions known for corresponding single-valued equations. This way the reader will be prepared for the more advanced study of multi-valued variational inequalities presented in Chapter 4. Applications to the existence of multiple and sign-changing solutions, to multi-valued equations with discontinuous multi-valued lower order bi-functions, and to generalized hemivariational inequalities are studied