Pub. Date:
Cambridge University Press
Nonlinear Analysis and Semilinear Elliptic Problems

Nonlinear Analysis and Semilinear Elliptic Problems

by Antonio Ambrosetti, Andrea Malchiodi


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Nonlinear Analysis and Semilinear Elliptic Problems

Many problems in science and engineering are described by nonlinear differential equations, which can be notoriously difficult to solve. Through the interplay of topological and variational ideas, methods of nonlinear analysis are able to tackle such fundamental problems. This graduate text explains some of the key techniques in a way that will be appreciated by mathematicians, physicists and engineers. Starting from elementary tools of bifurcation theory and analysis, the authors cover a number of more modern topics from critical point theory to elliptic partial differential equations. A series of Appendices give convenient accounts of a variety of advanced topics that will introduce the reader to areas of current research. The book is amply illustrated and many chapters are rounded off with a set of exercises.

Product Details

ISBN-13: 9780521863209
Publisher: Cambridge University Press
Publication date: 01/04/2007
Series: Cambridge Studies in Advanced Mathematics , #104
Pages: 328
Product dimensions: 5.98(w) x 8.98(h) x 0.83(d)

About the Author

Antonio Ambrosetti is a Professor at SISSA, Trieste.

Andrea Malchiodi is an Associate Professor at SISSA, Trieste.

Table of Contents

Preface; 1. Preliminaries; Part I. Topological Methods: 2. A primer on bifurcation theory; 3. Topological degree, I; 4. Topological degree, II: global properties; Part II. Variational Methods, I: 5. Critical points: extrema; 6. Constrained critical points; 7. Deformations and the Palais-Smale condition; 8. Saddle points and min-max methods; Part III. Variational Methods, II: 9. Lusternik-Schnirelman theory; 10. Critical points of even functionals on symmetric manifolds; 11. Further results on Elliptic Dirichlet problems; 12. Morse theory; Part IV. Appendices: Appendix 1. Qualitative results; Appendix 2. The concentration compactness principle; Appendix 3. Bifurcation for problems on Rn; Appendix 4. Vortex rings in an ideal fluid; Appendix 5. Perturbation methods; Appendix 6. Some problems arising in differential geometry; Bibliography; Index.

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