An Invitation to Variational Methods in Differential Equations - Softcover

Costa, David G.

Softcover

ISBN 10: 0817645357 ISBN 13: 9780817645359

Verlag: Birkhäuser Boston, 2007

Inhaltsangabe

This little book is a revised and expanded version of one I wrote for the "VIII Latin American School of Mathematics" [29], in Portuguese, based on which I have periodically taught a topics course over the last 18 years. As the - graduate students tle suggests, it is an introductory text. It is addressed to of mathematics in the area of differential equations/nonlinear analysis and to mathematicians in other areas who would like to have a first exposure to so called variational methods and their applications to PDEs and ODEs. Afterwards, the reader can choose from some excellent and more compreh- sive texts, which already exist in the literature but require somewhat more maturity in the area. We present a cross section of the area of variational methods, with a m- imum (no "pun" intended) of material, but clearly illustrating through one or two examples each of the results that we have chosen to present. So, besides the first motivating chapter and an appendix, there are only ten short chapters (with three or, at most, four sections each) through which the reader is quickly exposed to a few basic aspects of the beautiful area of variational methods and applications to differential equations. In fact, the reader may initially skip some of the more technical proofs of the main theorems, concentrating instead on the applications that are given.

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This book is a short introductory text to variational techniques with applications to differential equations. It presents a sampling of topics in critical point theory with applications to existence and multiplicity of solutions in nonlinear problems involving ordinary differential equations (ODEs) and partial differential equations (PDEs).

Five simple problems in ODEs which illustrate existence of solutions from a variational point of view are introduced in the first chapter. These problems set the stage for the topics covered, including minimization, deformation results, the mountain-pass theorem, the saddle-point theorem, critical points under constraints, a duality principle, critical points in the presence of symmetry, and problems with lack of compactness. Each topic is presented in a straightforward manner, and followed by one or two illustrative applications.

The concise, straightforward, user-friendly approach of this textbook will appeal to graduate students and researchers interested in differential equations, analysis, and functional analysis.

Details zur Ausgabe

• Verlag: Birkhäuser Boston
• Erscheinungsdatum: 2007
• Sprache: Englisch
• ISBN 10: 0817645357
• ISBN 13: 9780817645359
• Einband: Taschenbuch
• Anzahl der Seiten: 150
• Kontakt zum Hersteller: Springer Nature Customer Service Center GmbH; ProductSafety@springernature.com; ; Europaplatz 3; Heidelberg; 69115; Deutschland