Advances in Differential Equations

Morse index estimates for quasilinear equations on Riemannian manifolds

Silvia Cingolani, Giuseppina Vannella, and Daniela Visetti

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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.

Article information

Adv. Differential Equations, Volume 16, Number 11/12 (2011), 1001-1020.

First available in Project Euclid: 17 December 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 58E05: Abstract critical point theory (Morse theory, Ljusternik-Schnirelman (Lyusternik-Shnirel m an) theory, etc.) 35B20: Perturbations 35J60: Nonlinear elliptic equations 35J70: Degenerate elliptic equations


Cingolani, Silvia; Vannella, Giuseppina; Visetti, Daniela. Morse index estimates for quasilinear equations on Riemannian manifolds. Adv. Differential Equations 16 (2011), no. 11/12, 1001--1020.

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