On asymptotic expansions in nonlinear operator equations with applications to singular perturbation problems
Abstract
The paper deals with the existence and construction of formal asymptotic expansions of nonlinear functional equations and of the solutions of such equations. The starting point is the appropriate perturbed solution whose solution is known and where differentiability properties and inverse stability are satisfied. Unique solvability of the given problems and the existence of formal and asymptotic expansions are proved with the aid of the results of a perturbation theory for differentiable mappings due to Stummel (1976).
 Publication:

Zeitschrift Angewandte Mathematik und Mechanik
 Pub Date:
 March 1979
 Bibcode:
 1979ZaMM...59...38R
 Keywords:

 Asymptotic Methods;
 Nonlinear Equations;
 Operators (Mathematics);
 Perturbation Theory;
 Series Expansion;
 Singularity (Mathematics);
 Banach Space;
 Boundary Layers;
 Convergence;
 Uniqueness Theorem;
 Physics (General)