Asymptotic behavior of positive large solutions of semilinear Dirichlet problems
Let $\Omega $ be a smooth bounded domain in $\mathbb{R}^{n},\ n\geq 2$. This paper deals with the existence and the asymptotic behavior of positive solutions of the following problems \begin{equation*} \Delta u=a(x)u^{\alpha },\alpha >1\text{ and }\Delta u=a(x)e^{u}, \end{equation*} with the boun...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
University of Szeged
2013-09-01
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| Series: | Electronic Journal of Qualitative Theory of Differential Equations |
| Subjects: | |
| Online Access: | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=2512 |
| Summary: | Let $\Omega $ be a smooth bounded domain in $\mathbb{R}^{n},\ n\geq 2$. This paper deals with the existence and the asymptotic behavior of positive solutions of the following problems
\begin{equation*}
\Delta u=a(x)u^{\alpha },\alpha >1\text{ and }\Delta u=a(x)e^{u},
\end{equation*}
with the boundary condition $u_{\mid \partial \Omega }=+\infty .$ The weight function $a(x)$ is positive in $C_{loc}^{\gamma }(\Omega ),$ $0<\gamma <1$, and satisfies an appropriate assumption related to Karamata regular variation theory.
Our arguments are based on the sub-supersolution method. |
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| ISSN: | 1417-3875 |