David G. Costa

An Invitation to Variational Methods in Differential Equations (eBook, PDF)

• Format: PDF

Produktbeschreibung

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.

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Produktdetails

• Verlag: Springer Basel AG
• Seitenzahl: 138
• Erscheinungstermin: 30. April 2010
• Englisch
• ISBN-13: 9780817645366
• Artikelnr.: 37345239

Autorenporträt

David G. Costa, University of Nevada, Las Vegas, NV, USA

Inhaltsangabe

Critical Points Via Minimization.- The Deformation Theorem.- The Mountain-Pass Theorem.- The Saddle-Point Theorem.- Critical Points under Constraints.- A Duality Principle.- Critical Points under Symmetries.- Problems with an S1-Symmetry.- Problems with Lack of Compactness.- Lack of Compactness for Bounded ?.

Rezensionen

From the reviews:

"This book is intended to be an introduction to variational methods for ODEs and PDEs. ... Overall, this is a well-written book on the variational methods ... . The author clearly loves and knows the subject area and it is very good at providing an overview to the area ... . As such, a good guided reading course for graduate students could be made from this book, covering one chapter per session (or two)." (David A. W. Barton, Dynamical Systems Magazine, April, 2008)

"This little book consists of a very clear introduction to variational methods and their applications to ODEs and PDEs. ... the bibliography contains basic items on the subject and also turns out to be very useful for further reading. In my opinion the book should be strongly recommended to anyone-graduate student or researcher-who is interested in variational methods and their applications to differential equations." (Salvatore A. Marano, Mathematical Reviews, Issue 2008 k)

"The intention of the author is to provide a first introduction to variational methods in solving ODEs and PDEs for graduate students. The book is a concise collection of some fundamental aspects of this area ... . It presents a nice and direct approach to these central topics and is written with great care and clarity. It can be warmly recommended to anyone wishing to enter this active area of research." (M. Kunzinger, Monatshefte für Mathematik, Vol. 156 (4), April, 2009)