TY  - BOOK
AU  - Costa,David G.
ED  - SpringerLink (Online service)
TI  - An Invitation to Variational Methods in Differential Equations
SN  - 9780817645366
AV  - QA372 
U1  - 515.352 23
PY  - 2007///
CY  - Boston, MA
PB  - Birkhäuser Boston
KW  - Differential Equations
KW  - Mathematical optimization
KW  - Differential equations, partial
KW  - Ordinary Differential Equations
KW  - Calculus of Variations and Optimal Control; Optimization
KW  - Partial Differential Equations
N1  - 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 ?
N2  - 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
UR  - https://doi.org/10.1007/978-0-8176-4536-6
ER  -