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.
Rezensionen / Stimmen
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)
Sprache
Verlagsort
Verlagsgruppe
Illustrationen
9
9 s/w Abbildungen
XII, 138 p. 9 illus.
Dateigröße
ISBN-13
978-0-8176-4536-6 (9780817645366)
DOI
10.1007/978-0-8176-4536-6
Schweitzer Klassifikation
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 ?.
