Variational Methods for Strongly Indefinite Problems (Interdisciplinary Mathematical Sciences)

Ding, Yanheng

ISBN 10: 9812709622 / ISBN 13: 9789812709622

Published by World Scientific Publishing Company, 2007

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Bibliographic Details

• Title: Variational Methods for Strongly Indefinite Problems (Interdisciplinary Mathematical Sciences)
• Publisher: World Scientific Publishing Company
• Publication Date: 2007
• Language: English
• ISBN 10: 9812709622
• ISBN 13: 9789812709622
• Binding: Hardcover
• Condition: New

About this title

Synopsis

This unique book focuses on critical point theory for strongly indefinite functionals in order to deal with nonlinear variational problems in areas such as physics, mechanics and economics. With the original ingredients of Lipschitz partitions of unity of gage spaces (nonmetrizable spaces), Lipschitz normality, and sufficient conditions for the normality, as well as existence-uniqueness of flow of ODE on gage spaces, the book presents for the first time a deformation theory in locally convex topological vector spaces. It also offers satisfying variational settings for homoclinic-type solutions to Hamiltonian systems, Schrödinger equations, Dirac equations and diffusion systems, and describes recent developments in studying these problems. The concepts and methods used open up new topics worthy of in-depth exploration, and link the subject with other branches of mathematics, such as topology and geometry, providing a perspective for further studies in these areas. The analytical framework can be used to handle more infinite-dimensional Hamiltonian systems.

Review

This book contains a lot of material that can be useful for researchers in the field of critical point theory and its applications. --Zentralblatt MATH