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.
Some results on critical groups for a class of functionals defined on Sobolev Banach spaces
Cingolani Silvia;
2001-01-01
Abstract
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.File in questo prodotto:
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