Constrained mountain pass algorithm for the numerical solution of semilinear elliptic problems

摘要

A new numerical algorithm for solving semilinear elliptic problems is presented. A variational formulation is used and critical points of a C 1-functional subject to a constraint given by a level set of another C 1-functional (or an intersection of such level sets of finitely many functionals) are sought. First, constrained local minima are looked for, then constrained mountain pass points. The approach is based on the deformation lemma and the mountain pass theorem in a constrained setting. Several examples are given showing new numerical solutions in various applications.