Sidorov N., Loginov B., Sinitsyn A., Falaleev M. Lyapunov-Schmidt Methods in Nonlinear Analysis and Applications

Amsterdam: Springer, 2002. — 563 p.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.On Regularization of Linear Equations on the Basis of Perturbation Theory
Investigation of Bifurcation Points of a Nonlinear Equations
Regularization of Computation of Solutions in a Neighborhood of the Branch Point
Iterations, Interlaced Equations, and Lyapunov Convex Majorants in Nonlinear Analysis
Methods of Representation Theory and Group Analysis in Bifurcation Theory
Singular Differential Equations in Banach Spaces
Steady-State Solutions of the Vlasov—Maxwell System