Special Session 41: Topological and Variational Methods for Multivalued Differential Equations

Multivalued differential equations arise naturally in various branches of modern mathematics, indeed they play a significant role in the description of processes in control theory and non-smooth analysis. Due to their wide applicability in physics, biology, chemistry, and economics, there has recently been an increasing interest in this field. The aim of this Special Session is to outline the recent progress on the field of differential inclusions, both in infinite and finite dimensional spaces. In particular, topics of interest are control problems, non-smooth variational analysis, differential equations with discontinuous nonlinearities, functional inclusions, nonlocal problems, and boundary value problems in bounded and unbounded domains. Due to the diversity of applications and the variety of problems, there is a wide range of methods and techniques available. In this Session, both variational methods (e.g. critical point theory, linking theorems) as well as topological methods (e.g. fixed points theorems, lower and upper solutions, topological degree) will be presented and discussed.