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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

Zhijun Zhang 1,

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 $\partial\Omega$.
Keywords: nonlinear gradient terms, the asymptotic behaviour., Semilinear elliptic equations, large solutions.
Mathematics Subject Classification: Primary: 35J60, 35B25; Secondary: 35B50, 35R0.
Citation: Zhijun Zhang. Boundary blow-up for elliptic problems involving exponential nonlinearities with nonlinear gradient terms and singular weights. Communications on Pure & Applied Analysis, 2007, 6 (2) : 521-529. doi: 10.3934/cpaa.2007.6.521
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