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

Summary. A new numerical algorithm for solving semilinear elliptic problems is presented. A variational formulation is used and critical points of a C¹-functional subject to a constraint given by a level set of another C¹-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.Mathematics Subject Classification (2000):35J20, 65N99The author would like to thank the referee for helpful comments in particular on Section 4.