Perturbed bifurcation in the von Kármán equations

Abstract

An asymptotic method is presented to analyse perturbations of bifurcations of the solutions of nonlinear problems. The perturbations may result from imperfections, impurities or other inhomogeneities in the corresponding physical problem. Using a method of matched asymptotic expansions we obtain global representations of the solutions of the perturbed problem when the bifurcation solutions are known globally. Even if, in this paper, the asymptotic method is used to analyse the perturbed bifurcation in the von Kármán equations, the same analysis is also valid to study the perturbations in more general nonlinear problems.