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.

Contenuti

Preface. 1. On Regularization of Linear Equations on the Basis of Perturbation Theory. 2. Investigation of Bifurcation Points of a Nonlinear Equations. 3. Regularization of Computation of Solutions in a Neighborhood of the Branch Point. 4. Iterations, Interlaced Equations and Lyapunov Conbex Majorants in Nonlinear Analysis. 5. Methods of Representation Theory and Group Analysis in Bifurcation Theory. 6. Singular Differential Equations in Banach Spaces. 7. Steady-State Solutions of the Vlasov-Maxwell System. Appendices. A: Positive solutions of the nonlinear singular boundary value problem of magnetic insulation. References. Index.

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