Nonlinear Analysis and Semilinear Elliptic...

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Sprache: Englisch

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Beschreibung

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.

Über den Autor

Antonio Ambrosetti is a Professor at SISSA, Trieste.

Zusammenfassung

Many problems in science and engineering are described by nonlinear differential equations, which can be notoriously difficult to solve. Methods of nonlinear analysis are able to tackle such fundamental problems and 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. The book is amply illustrated with many exercises.

Inhaltsverzeichnis

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.

Details

Medium:	Buch
Seiten:	330
ISBN-13:	9780521863209
ISBN-10:	0521863201
Sprache:	Englisch
Ausstattung / Beilage:	HC gerader Rücken kaschiert
Einband:	Gebunden
Autor:	Ambrosetti, Antonio
Hersteller:	Cambridge University Press
Maße:	235 x 157 x 22 mm
Von/Mit:	Antonio Ambrosetti
Erscheinungsdatum:	04.01.2007
Gewicht:	0,632 kg

preigu-id: 102131992

Über den Autor

Antonio Ambrosetti is a Professor at SISSA, Trieste.

Zusammenfassung

Inhaltsverzeichnis

Details

Medium:	Buch
Seiten:	330
ISBN-13:	9780521863209
ISBN-10:	0521863201
Sprache:	Englisch
Ausstattung / Beilage:	HC gerader Rücken kaschiert
Einband:	Gebunden
Autor:	Ambrosetti, Antonio
Hersteller:	Cambridge University Press
Maße:	235 x 157 x 22 mm
Von/Mit:	Antonio Ambrosetti
Erscheinungsdatum:	04.01.2007
Gewicht:	0,632 kg