Differential and Integral Equations

Existence results for a nonlinear elliptic equation with critical Sobolev exponent

Mohamed Ben Ayed and Hichem Chtioui

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text


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.

Article information

Differential Integral Equations, Volume 18, Number 1 (2005), 1-18.

First available in Project Euclid: 21 December 2012

Permanent link to this document

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35J60: Nonlinear elliptic equations
Secondary: 35B33: Critical exponents 47J30: Variational methods [See also 58Exx]


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

Export citation