Some results on critical groups for a class of functionals defined on Sobolev Banach spaces

We present critical groups estimates for a functional f defined on the Banach space $W_0^{1,p}(Ω)$, where Ω is a bounded domain in R^N, p>2, associated to a quasilinear elliptic equation involving p-laplacian. In spite of the lack of an Hilbert structure and of Fredholm property of the second order differential of f in each critical point, we compute the critical groups of f in each isolated critical point via Morse index.