Nonlinear Functional Analysis: A First Course

The book discusses the basic theory of topological and variational methods used in solving nonlinear equations involving mappings between normed linear spaces. It is meant to be a primer of nonlinear analysis and is designed to be used as a text or reference book by graduate students. Frechet derivative, Brouwer fixed point theorem, Borsuk's theorem, and bifurcation theory along with their applications have been discussed. Several solved examples and exercises have been carefully selected and included in the present edition. The prerequisite for following this book is the basic knowledge of functional analysis and topology.

Auteur

S. Kesavan is Adjunct Professor at the Indian Institute of Technology Madras, Chennai, India. He received his Docteur-es-Sciences Mathematiques from the Universite Pierre et Marie Curie (Paris VI) in 1979 for the thesis entitled Sur l'approximation de probl`emes lineaires et nonlineaires de valeurs propres, supervised by Professors J.L. Lions and P.G. Ciarlet. Earlier, he served as Professor at the Institute of Mathematical Sciences, Chennai, India, and Deputy Director at Chennai Mathematical Institute, India. His research areas include partial differential equations, homogenization, control theory, and isoperimetric inequalities. Author of 5 books, Prof. Kesavan has published over 50 papers in national and international journals in addition to several contributions to conference proceedings. He was elected Vice-President of the Ramanujan Mathematical Society in 2019 and Fellow of the Indian Academy of Sciences, Bangalore, in 2008. He is the recipient of the C.L. Chandna Award for Outstanding Contributions to Mathematics Research and Teaching (1999) and Tamil Nadu Scientist Award (TANSA), awarded by the Tamil Nadu State Council for Science and Technology, in Mathematical Sciences (1998).

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Contenu

1. Differential Calculus on Normed Linear Spaces.- 2. The Brouwer Degree.- 3. The Leray-Schauder Degree.- 4. Bifurcation Theory.- 5. Critical Points of Functionals.