Lyapunov-Schmidt Methods in Nonlinear Analysis and Applications
Lyapunov-Schmidt Methods in Nonlinear Analysis and Applications By Nikolay Sidorov, Boris Loginov, Aleksandr Sinitsyn, Michail Falaleev (auth.)
2002 | 548 Pages | ISBN: 9048161509 | PDF | 20 MB
2002 | 548 Pages | ISBN: 9048161509 | PDF | 20 MB
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.