Multiple critical points for asymptotically quadratic functionals

This work establishes conditions for the existence of nonzero critical points for asymptotically quadratic functionals defined in real Hilbert spaces. Our concern is the study of situations where the associated quadratic form is degenerate. The technique used combines perturbation arguments, a construction associated with the existence of Linking subsets, and Morse index estimate. The results obtained are applied to the existence of multiple solutions for semilinear elliptic problems.