### Least energy solutions for critical growth equations with a lower order perturbation

Alberto Ferrero

#### Abstract

We study existence and nonexistence of least energy solutions of a quasilinear critical growth equation with degenerate $m$-Laplace operator in a bounded domain in $\mathbb{R}^n$ with $n>m>1$. Existence and nonexistence of solutions of this problem depend on a lower order perturbation and on the space dimension $n$. Our proofs are obtained with critical point theory and the lack of compactness, due to critical growth condition, is overcome by constructing minimax levels in a suitable compactness range.

#### Article information

Source
Adv. Differential Equations Volume 11, Number 10 (2006), 1167-1200.

Dates
First available in Project Euclid: 18 December 2012