TY  - JOUR
ID  - Chaieb2016
LB  - Chaieb2016
AU  - Chaieb, Majda
AU  - Dhifli, Abdelwaheb
AU  - Zermani, Samia
TI  - Existence and asymptotic behavior of positive solutions of a semilinear elliptic system in a bounded domain
ST  - Existence and asymptotic behavior of positive solutions of a semilinear elliptic system in a bounded domain
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2016
VL  - 36
IS  - 3
SP  - 315
EP  - 336
DO  - http://dx.doi.org/10.7494/OpMath.2016.36.3.315
UR  - http://dx.doi.org/10.7494/OpMath.2016.36.3.315
AB  - 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.
KW  - semilinear elliptic system
KW  - asymptotic behavior
KW  - Karamata class
KW  - sub-super solution
SN  - 1232-9274
ER  -