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题名/责任者:

Index theory in nonlinear analysis / Chungen Liu = 非线性分析的指标理论 / 刘春根.

出版发行项:

Beijing : Science Press, [2019]

出版发行项:

?2019

ISBN:

9787030595669 (hardback)

载体形态项:

xix, 333 pages ; 25 cm.

变异题名:

非线性分析的指标理论

丛编说明:

Mathematics monograph series ; 38

个人责任者:

Liu, Chungen author.

论题主题:

Nonlinear functional analysis.

论题主题:

Index theory (Mathematics)

中图法分类号:

O177.91

一般附注:

"Supported by the National Fund for Academic Publication in Science and Technology"

书目附注:

Includes bibliographical references (pages [319]-330)and index.

内容附注:

Linear Algebraic Aspects -- A brief introduction to index functions -- Relative Morse index -- The P-index theory -- The L-index theory -- Maslov type index for Lagrangian paths -- Revisit of Maslov type index for Symplectic Paths -- Applications of P-index -- Applications of L-index -- Multiplicity of brake orbits on a fixed energy surface -- The existence and multiplicity of solutions of wave equations.

摘要附注:

This book provides detailed information on index theories and their applications, especially Maslov-type index theories and their iteration theories for non-periodic solutions of Hamiltonian systems. It focuses on two index theories: L-index theory (index theory for Lagrangian boundary conditions) and P-index theory (index theory for P-boundary conditions). In addition, the book introduces readers to recent advances in the study of index theories for symmetric periodic solutions of nonlinear Hamiltonian systems, and for selected boundary value problems involving partial differential equations.

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