Topology and Nonlinear Boundary Value Problems

Abstract

This chapter highlights the topology and nonlinear boundary value problems. Topological arguments, in particular degree theory, are now quite classical in existence problems for nonlinear equations. During the past few decades, progress in this field has followed very closely, and often suggested, the development of some parts of topology. The chapter explains how techniques in ordinary, functional and partial differential equations can mutually influence each other when integrated in a common abstract scheme. It presents mapping theorems for quasi-bounded perturbations of linear Fredholm operators and also presents the periodic solutions of ordinary and functional differential equations.