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Variational Methods for Strongly Indefinite Problems

Interdisciplinary Mathematical Sciences v. 7

By (author) Yanheng Ding
Format: Hardback
Publisher: World Scientific Publishing Co Pte Ltd, Singapore, Singapore
Published: 15th Aug 2007
Dimensions: w 175mm h 247mm d 17mm
Weight: 531g
ISBN-10: 9812709622
ISBN-13: 9789812709622
Barcode No: 9789812709622
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, Schrodinger 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.

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