Morse index estimates for quasilinear equations on Riemannian manifolds

Abstract

This work deals with Morse index estimates for a solution $ u\in H_1^p(M)$ of the quasilinear elliptic equation $ -\textrm{div}_g \big ( \big (\alpha +|\nabla u|_g^2 \big )^{(p-2)/2}\nabla u \big )=h(x,u) $, where $(M,g)$ is a compact, Riemannian manifold, $0 < \alpha$, $2 \leq p < n$. The nonlinear right-hand side $h(x,s)$ is allowed to be subcritical or critical.