Lyapunov Schmidt Methods In Nonlinear Analysis And Applications

Lyapunov-Schmidt Methods in Nonlinear Analysis and Applications

Recent theory and applications of the Lyapunov-Shmidt method are presented in this specialized volume of use to mathematicians, physicists, and engineers interested in nonlinear equations. The chapters describe the Lyapunov-Shmidt method and its use for obtaining branching solutions for nonlinear equations using iterative techniques, techniques for constructing regularizing equations, the use of power geometry methods, the theory of branching for interlaced equations, applications of ideas of symmetry in the theory of bifurcations, applications in differential operator equations, and applied problems of mathematical physics. The four authors are Russian mathematicians who teach at the Irkutsk State U and the Ulyanovsk State Technical U. in Russia and the National U. of Colombia in Bogota. Annotation (c)2003 Book News, Inc., Portland, OR (booknews.com).

Lyapunov-Schmidt Methods in Nonlinear Analysis and Applications

Lyapunov-Schmidt Methods in Nonlinear Analysis and Applications

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.