Degree Theory for Discontinuous Operators : Applications to Discontinuous Differential Equations (Rsme Springer Series)

Figueroa Sestelo, Rubén/ López Pouso, Rodrigo/ Rodríguez López, Jorge

Springer Nature Switzerland AG（2022/09発売）

• 製本 Paperback:紙装版/ペーパーバック版／ページ数 190 p.
• 商品コード 9783030816063

Full Description

This unique book contains a generalization of the Leray-Schauder degree theory which applies for wide and meaningful types of discontinuous operators. The discontinuous degree theory introduced in the first section is subsequently used to prove new, applicable, discontinuous versions of many classical fixed-point theorems such as Schauder's. Finally, readers will find in this book several applications of those discontinuous fixed-point theorems in the proofs of new existence results for discontinuous differential problems. Written in a clear, expository style, with the inclusion of many examples in each chapter, this book aims to be useful not only as a self-contained reference for mature researchers in nonlinear analysis but also for graduate students looking for a quick accessible introduction to degree theory techniques for discontinuous differential equations.

Contents

- 1. Introduction. - 2. Degree Theory for a Class of Discontinuous Operators. - 3. Fixed Point Theorems for Some Discontinuous Operators. - 4. First Order Problems. - 5. Second Order Problems and Lower and Upper Solutions. - 6. Positive Solutions for Second and Higher Order Problems.