@Article{Chaieb2016,
author = "Chaieb, Majda and Dhifli, Abdelwaheb and Zermani, Samia",
title = "Existence and asymptotic behavior of positive solutions of a semilinear elliptic system in a bounded domain",
journal = "Opuscula Math.",
year = "2016",
volume = "36",
number = "3",
pages = "315--336",
doi = "http://dx.doi.org/10.7494/OpMath.2016.36.3.315",
url = "http://dx.doi.org/10.7494/OpMath.2016.36.3.315",
abstract = "Let \(\Omega\) be a bounded domain in \(\mathbb{R}^{n}\) (\(n\geq 2\)) with a smooth boundary \(\partial \Omega\). We discuss in this paper the existence and the asymptotic behavior of positive solutions of the following semilinear elliptic system \[\begin{aligned} -\Delta u&=a_{1}(x)u^{\alpha}v^{r}\quad\text{in}\;\Omega ,\;\;\,u|_{\partial\Omega}=0,\\ -\Delta v&=a_{2}(x)v^{\beta}u^{s}\quad\text{in}\;\Omega ,\;\;\,v|_{\partial\Omega }=0.\end{aligned}\] Here \(r,s\in \mathbb{R}\), \(\alpha,\beta \lt 1\) such that \(\gamma :=(1-\alpha)(1-\beta)-rs\gt 0\) and the functions \(a_{i}\) (\(i=1,2\)) are nonnegative and satisfy some appropriate conditions with reference to Karamata regular variation theory.",
keywords = "semilinear elliptic system, asymptotic behavior, Karamata class, sub-super solution",
issn = "1232-9274"
}