Lyapunov-Schmidt Methods in Nonlinear Analysis and Applications

✍ Scribed by Nikolay Sidorov, Boris Loginov, Aleksandr Sinitsyn, Michail Falaleev (auth.)

• Publisher: Springer Netherlands
• Year: 2002
• Tongue: English
• Leaves: 563
• Series: Mathematics and Its Applications 550
• Edition: 1
• Category: Library

✦ Synopsis

This book concentrates on the branching solutions of nonlinear operator equations and the theory of degenerate operator-differential equations especially applicable to algorithmic analysis and nonlinear PDE's in mechanics and mathematical physics.
The authors expound the recent result on the generalized eigen-value problem, the perturbation method, Schmidt's pseudo-inversion for regularization of linear and nonlinear problems in the branching theory and group methods in bifurcation theory. The book covers regular iterative methods in a neighborhood of branch points and the theory of differential-operator equations with a non-invertible operator in the main expression is constructed. Various recent results on theorems of existence are given including asymptotic, approximate and group methods.

✦ Table of Contents

Front Matter....Pages i-xx
On Regularization of Linear Equations on the Basis of Perturbation Theory....Pages 1-42
Investigation of Bifurcation Points of a Nonlinear Equations....Pages 43-97
Regularization of Computation of Solutions in a Neighborhood of the Branch Point....Pages 99-150
Iterations, Interlaced Equations, and Lyapunov Convex Majorants in Nonlinear Analysis....Pages 151-216
Methods of Representation Theory and Group Analysis in Bifurcation Theory....Pages 217-336
Singular Differential Equations in Banach Spaces....Pages 337-430
Steady-State Solutions of the Vlasov—Maxwell System....Pages 431-495
Back Matter....Pages 497-548

✦ Subjects

Partial Differential Equations; Functional Analysis; Algorithms; Mathematical Modeling and Industrial Mathematics; Applications of Mathematics