Topological Degree with Applications

by Giovanni Vidossich

Overview

This book is unique in the current scenario because it provides a complete treatment of modern Brouwer and of Leray-Schauder degree theories, including detailed proofs and selected applications to differential equations. In addition, new results and open problems appear throughout. It aims to introduce Ph.D. students to research on nonlinear boundary value problems for ordinary, elliptic, and evolution equations using the topological methods of nonlinear functional analysis. It is suitable for self-study, as all proofs are detailed, with prerequisites provided when necessary. It is based on personal notes compiled over more than forty years of teaching.

Product Details

ISBN-13:	9783031929977
Publisher:	Springer Nature Switzerland
Publication date:	09/01/2025
Series:	SISSA Springer Series , #6
Pages:	545
Product dimensions:	6.10(w) x 9.25(h) x (d)

About the Author

GV studied mathematics in Pisa during the 1960s with G. Stampacchis as Supervisor. He has been Professor at the Universities of Brasilia and Trieste, ending his career at SISSA (the research institute he co-founded together with P. Budinich, L. Fonda and L. Stasi). He has held visiting positions in Brazil, Peru, Somalia, South Africa and USA. After an initial activity in general topology, his main research topic has become BVPs for ODEs in connection with the topological methods of nonlinear functional analysis.

Table of Contents

The theory.- Applications to the topology of RN.- Applications to fixed point theory.- Applications to ODEs.