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Minimax Systems and Critical Point Theory

2009-05-28 Mathematics
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Release : 2009-05-28
Genre : Mathematics
Kind : eBook
Book Rating : 026/5 ( reviews)

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Book Synopsis Minimax Systems and Critical Point Theory by : Martin Schechter

Download or read book Minimax Systems and Critical Point Theory written by Martin Schechter. This book was released on 2009-05-28. Available in PDF, EPUB and Kindle. Book excerpt: This text starts at the foundations of the field, and is accessible with some background in functional analysis. As such, the book is ideal for classroom of self study. The new material covered also makes this book a must read for researchers in the theory of critical points.

Minimax Methods in Critical Point Theory with Applications to Differential Equations

1986-07-01 Mathematics
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Release : 1986-07-01
Genre : Mathematics
Kind : eBook
Book Rating : 153/5 ( reviews)

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Book Synopsis Minimax Methods in Critical Point Theory with Applications to Differential Equations by : Paul H. Rabinowitz

Download or read book Minimax Methods in Critical Point Theory with Applications to Differential Equations written by Paul H. Rabinowitz. This book was released on 1986-07-01. Available in PDF, EPUB and Kindle. Book excerpt: The book provides an introduction to minimax methods in critical point theory and shows their use in existence questions for nonlinear differential equations. An expanded version of the author's 1984 CBMS lectures, this volume is the first monograph devoted solely to these topics. Among the abstract questions considered are the following: the mountain pass and saddle point theorems, multiple critical points for functionals invariant under a group of symmetries, perturbations from symmetry, and variational methods in bifurcation theory. The book requires some background in functional analysis and differential equations, especially elliptic partial differential equations. It is addressed to mathematicians interested in differential equations and/or nonlinear functional analysis, particularly critical point theory.

Critical Point Theory and the Minimax Principle

196?
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Release : 196?
Genre :
Kind : eBook
Book Rating : /5 ( reviews)

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Book Synopsis Critical Point Theory and the Minimax Principle by : Richard S. Palais

Download or read book Critical Point Theory and the Minimax Principle written by Richard S. Palais. This book was released on 196?. Available in PDF, EPUB and Kindle. Book excerpt:

Critical Point Theory and Its Applications

2006-09-10 Mathematics
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Release : 2006-09-10
Genre : Mathematics
Kind : eBook
Book Rating : 684/5 ( reviews)

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Book Synopsis Critical Point Theory and Its Applications by : Wenming Zou

Download or read book Critical Point Theory and Its Applications written by Wenming Zou. This book was released on 2006-09-10. Available in PDF, EPUB and Kindle. Book excerpt: This book presents some of the latest research in critical point theory, describing methods and presenting the newest applications. Coverage includes extrema, even valued functionals, weak and double linking, sign changing solutions, Morse inequalities, and cohomology groups. Applications described include Hamiltonian systems, Schrödinger equations and systems, jumping nonlinearities, elliptic equations and systems, superlinear problems and beam equations.

Critical Point Theory and Hamiltonian Systems

2013-04-17 Science
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Release : 2013-04-17
Genre : Science
Kind : eBook
Book Rating : 610/5 ( reviews)

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Book Synopsis Critical Point Theory and Hamiltonian Systems by : Jean Mawhin

Download or read book Critical Point Theory and Hamiltonian Systems written by Jean Mawhin. This book was released on 2013-04-17. Available in PDF, EPUB and Kindle. Book excerpt: FACHGEB The last decade has seen a tremendous development in critical point theory in infinite dimensional spaces and its application to nonlinear boundary value problems. In particular, striking results were obtained in the classical problem of periodic solutions of Hamiltonian systems. This book provides a systematic presentation of the most basic tools of critical point theory: minimization, convex functions and Fenchel transform, dual least action principle, Ekeland variational principle, minimax methods, Lusternik- Schirelmann theory for Z2 and S1 symmetries, Morse theory for possibly degenerate critical points and non-degenerate critical manifolds. Each technique is illustrated by applications to the discussion of the existence, multiplicity, and bifurcation of the periodic solutions of Hamiltonian systems. Among the treated questions are the periodic solutions with fixed period or fixed energy of autonomous systems, the existence of subharmonics in the non-autonomous case, the asymptotically linear Hamiltonian systems, free and forced superlinear problems. Application of those results to the equations of mechanical pendulum, to Josephson systems of solid state physics and to questions from celestial mechanics are given. The aim of the book is to introduce a reader familiar to more classical techniques of ordinary differential equations to the powerful approach of modern critical point theory. The style of the exposition has been adapted to this goal. The new topological tools are introduced in a progressive but detailed way and immediately applied to differential equation problems. The abstract tools can also be applied to partial differential equations and the reader will also find the basic references in this direction in the bibliography of more than 500 items which concludes the book. ERSCHEIN

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