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Index theory in nonlinear analysis

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Index theory in nonlinear analysis/ by Chungen Liu.
Author:	Liu, Chungen.
Description:	XXI, 333 p. 94 illus.online resource. :
Contained By:	Springer Nature eBook
Subject:	Dynamics. -
Online resource:	https://doi.org/10.1007/978-981-13-7287-2
ISBN:	9789811372872

Index theory in nonlinear analysis
Liu, Chungen.

Index theory in nonlinear analysis[electronic resource] /by Chungen Liu. - 1st ed. 2019. - XXI, 333 p. 94 illus.online resource.

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.

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.

ISBN: 9789811372872

Standard No.: 10.1007/978-981-13-7287-2doiSubjects--Topical Terms:

592238
Dynamics.

LC Class. No.: QA313

Dewey Class. No.: 515.39

Index theory in nonlinear analysis
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505 0 $a 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.
520 $a 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.
650 0 $a Dynamics. $3 592238
650 0 $a Ergodic theory. $3 672355
650 0 $a Differential equations. $3 527664
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650 2 4 $a Ordinary Differential Equations. $3 670854
650 2 4 $a Differential Geometry. $3 671118
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