Index theory in nonlinear analysis

Beschreibung

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.

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.

Autor*in

Chungen Liu

Themen in »Index theory in nonlinear analysis«

Maslov type index Morse index P-index L-index nonlinear Hamiltonian systems existence and multiplicity of solutions of wave equations Lagrangian paths ordinary differential equations

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“This book provides a very lucid and versatile introduction to the methods of index theories and their applications. It covers very important material in a concise and very instructive manner, and as such, it may serve as an excellent guide to further, more advanced and detailed reading in this area of mathematics.” (Ahmed Lesfari, zbMATH 1420.37001, 2019)

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