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

Cingolani, Silvia ; Vannella, Giuseppina

Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni, Série 9, Tome 12 (2001) no. 4, pp. 199-203

Résumé

We present critical groups estimates for a functional $f$ defined on the Banach space $W^{1,p}_{0}(\Omega)$, $\Omega$ bounded domain in $\mathbb{R}^{N}$, $2 p \infty$, 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.