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An Invitation to Variational Methods in Differential Equations

By: Costa, David G [author.].
Contributor(s): SpringerLink (Online service)0.
Material type: materialTypeLabelBookPublisher: Boston, MA : Birkh�user Boston, 2007. Description: XII, 138 p. 9 illus. online resource.Content type: text Media type: computer Carrier type: online resourceISBN: 9780817645366.Subject(s): Mathematics | Differential equations | Partial differential equations | Calculus of variations.1 | Mathematics.2 | Ordinary Differential Equations.2 | Calculus of Variations and Optimal Control; Optimization.2 | Partial Differential Equations.2DDC classification: 515.352 Online resources: Click here to access online
Contents:
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 ?.
In: Springer eBooks0Summary: 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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PK Kelkar Library, IIT Kanpur
Available EBK9230
Total holds: 0

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 ?.

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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