Abstract
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.
Citation
Mohamed Ben Ayed. Hichem Chtioui. "Existence results for a nonlinear elliptic equation with critical Sobolev exponent." Differential Integral Equations 18 (1) 1 - 18, 2005. https://doi.org/10.57262/die/1356060233
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