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Critical Point Theory and Its Applications [electronic resource] /by Wenming Zou, Martin Schechter.

by Zou, Wenming [author.]; Schechter, Martin [author.]; SpringerLink (Online service).
Material type: materialTypeLabelBookPublisher: Boston, MA : Springer US, 2006.Description: XII, 318 p. online resource.ISBN: 9780387329680.Subject(s): Mathematics | Functional analysis | Global analysis | Differential Equations | Differential equations, partial | Mathematics | Global Analysis and Analysis on Manifolds | Partial Differential Equations | Ordinary Differential Equations | Functional AnalysisDDC classification: 514.74 Online resources: Click here to access online
Contents:
Preliminaries -- Functionals Bounded Below -- Even Functionals -- Linking and Homoclinic Type Solutions -- Double Linking Theorems -- Superlinear Problems -- Systems with Hamiltonian Potentials -- Linking and Elliptic Systems -- Sign-Changing Solutions -- Cohomology Groups.
In: Springer eBooksSummary: Since the birth of the calculus of variations, researchers have discovered that variational methods, when they apply, can obtain better results than most other methods. Moreover, they apply in a very large number of situations. It was realized many years ago that the solutions of a great number of problems are in effect critical points of functionals. Critical Point Theory and Its Applications presents some of the latest research in the area of critical point theory. Researchers have obtained many new results recently using this approach, and in most cases comparable results have not been obtained with other methods. This book describes the methods and presents the newest applications. The topics covered in the book include extrema, even valued functionals, weak and double linking, sign changing solutions, Morse inequalities, and cohomology groups. The applications described include Hamiltonian systems, Schrödinger equations and systems, jumping nonlinearities, elliptic equations and systems, superlinear problems and beam equations. Many minimax theorems are established without the use of the (PS) compactness condition. Audience This book is intended for advanced graduate students and researchers in mathematics studying the calculus of variations, differential equations and topological methods.
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Preliminaries -- Functionals Bounded Below -- Even Functionals -- Linking and Homoclinic Type Solutions -- Double Linking Theorems -- Superlinear Problems -- Systems with Hamiltonian Potentials -- Linking and Elliptic Systems -- Sign-Changing Solutions -- Cohomology Groups.

Since the birth of the calculus of variations, researchers have discovered that variational methods, when they apply, can obtain better results than most other methods. Moreover, they apply in a very large number of situations. It was realized many years ago that the solutions of a great number of problems are in effect critical points of functionals. Critical Point Theory and Its Applications presents some of the latest research in the area of critical point theory. Researchers have obtained many new results recently using this approach, and in most cases comparable results have not been obtained with other methods. This book describes the methods and presents the newest applications. The topics covered in the book include extrema, even valued functionals, weak and double linking, sign changing solutions, Morse inequalities, and cohomology groups. The applications described include Hamiltonian systems, Schrödinger equations and systems, jumping nonlinearities, elliptic equations and systems, superlinear problems and beam equations. Many minimax theorems are established without the use of the (PS) compactness condition. Audience This book is intended for advanced graduate students and researchers in mathematics studying the calculus of variations, differential equations and topological methods.

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