Existence and asymptotic behavior of positive solutions of a semilinear elliptic system in a bounded domain
| Autor: | Samia Zermani, Majda Chaieb, Abdelwaheb Dhifli |
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| Rok vydání: | 2016 |
| Předmět: |
semilinear elliptic system
sub-super solution Discrete mathematics lcsh:T57-57.97 General Mathematics 010102 general mathematics Boundary (topology) Karamata class 01 natural sciences Omega Variation theory Delta-v (physics) 010101 applied mathematics Bounded function lcsh:Applied mathematics. Quantitative methods Domain (ring theory) asymptotic behavior 0101 mathematics Mathematics |
| Zdroj: | Opuscula Mathematica, Vol 36, Iss 3, Pp 315-336 (2016) |
| ISSN: | 1232-9274 |
| DOI: | 10.7494/opmath.2016.36.3.315 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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