An invitation to variational methods in differential equations

Abstract

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. © 2007 Birkhäuser Boston. All rights reserved.