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Index theory in nonlinear analysis de Chungen Liu

Index theory in nonlinear analysis

Autor Chungen Liu
en Limba Engleză Paperback – 15 aug 2020
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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Specificații

ISBN-13: 9789811372896
ISBN-10: 9811372896
Pagini: 333
Ilustrații: XXI, 333 p. 94 illus.
Dimensiuni: 155 x 235 mm
Ediția:1st ed. 2019
Editura: Springer Nature Singapore
Colecția Springer
Locul publicării:Singapore, Singapore

Cuprins

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.

Recenzii

“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)

Textul de pe ultima copertă

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.

Caracteristici

Equip readers with both L-index theory and P-index theory Demonstrate recent progress on index theories for a symmetric periodic solution of nonlinear Hamiltonian systems