$$H^ 1$$ versus $$C^ 1$$ isolated critical points.(English. Abridged French version)Zbl 0810.35025

Summary: We prove the coincidence of the critical groups for isolated critical points in the topologies $$C^ 1$$ and $$H^ 1$$ for functionals related to second order semilinear elliptic boundary value problems on bounded domains. An example is provided in showing how it is used in the study of multiple solutions.

MSC:

 35J65 Nonlinear boundary value problems for linear elliptic equations 46M20 Methods of algebraic topology in functional analysis (cohomology, sheaf and bundle theory, etc.) 35J20 Variational methods for second-order elliptic equations