# American Institute of Mathematical Sciences

June  2007, 6(2): 521-529. doi: 10.3934/cpaa.2007.6.521

## Boundary blow-up for elliptic problems involving exponential nonlinearities with nonlinear gradient terms and singular weights

 1 Department of Mathematics and Informational Science, Yantai University, P.O. Box 264005, Yantai, Shandong, China

Received  March 2006 Revised  August 2006 Published  March 2007

By a perturbation method and constructing comparison functions, we show the exact asymptotic behaviour of solutions near the boundary to nonlinear elliptic problems Δ$u\pm|\nabla u|^q=b(x)e^u,\ x \in \Omega, \ u|_{\partial \Omega}=\infty,$ where $\Omega$ is a bounded domain with smooth boundary in $\mathbb R^N$, $q \geq 0$, $b$ is non-negative in $\Omega$ and singular on $\partial\Omega$.
Citation: Zhijun Zhang. Boundary blow-up for elliptic problems involving exponential nonlinearities with nonlinear gradient terms and singular weights. Communications on Pure and Applied Analysis, 2007, 6 (2) : 521-529. doi: 10.3934/cpaa.2007.6.521
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