Differential and Integral Equations
- Differential Integral Equations
- Volume 18, Number 1 (2005), 1-18.
Existence results for a nonlinear elliptic equation with critical Sobolev exponent
In this paper we study the following nonlinear elliptic problem with Dirichlet boundary condition: $-\Delta u =K(x)u^p$, $u>0$ in $\Omega$, $u =0$ on $ \partial \Omega$, where $\Omega$ is a bounded, smooth domain of $\mathbb R^n$, $n\geq 4$ and $p+1=2n/(n-2)$ is the critical Sobolev exponent. Using dynamical and topological methods involving the study of the critical points at infinity of the associated variational problem, we prove some existence results.
Differential Integral Equations, Volume 18, Number 1 (2005), 1-18.
First available in Project Euclid: 21 December 2012
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Ben Ayed, Mohamed; Chtioui, Hichem. Existence results for a nonlinear elliptic equation with critical Sobolev exponent. Differential Integral Equations 18 (2005), no. 1, 1--18. https://projecteuclid.org/euclid.die/1356060233