CRITICAL GROUPS AT INFINITY, SADDLE POINT REDUCTION AND ELLIPTIC RESONANT PROBLEMS
Shibo Liu, Shujie Li · Communications in Contemporary Mathematics · 2003
We prove that if the Lyapunov–Schmidt method is applicable, then the critical groups at infinity of the reduced functional are isomorphic to those of the original functional. This observation, combining with our results on the critical groups of finite dimensional functional, enables us to compute the critical groups at infinity. New multiplicity results for resonant elliptic boundary value problems are obtained as applications.