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EXISTENCE OF LARGE SOLUTIONS FOR A QUASILINEAR ELLIPTIC PROBLEM  

Sun, Yan (Institute of Mathematics, School of Mathematics Science, Nanjing Normal University)
Yang, Zuodong (Institute of Mathematics, School of Mathematics Science, Nanjing Normal University, College of Zhongbei, Nanjing Normal University)
Publication Information
Journal of applied mathematics & informatics / v.28, no.1_2, 2010 , pp. 217-231 More about this Journal
Abstract
We consider a class of elliptic problems of a logistic type $$-div(|{\nabla}_u|^{m-2}{\nabla}_u)\;=\;w(x)u^q\;-\;(a(x))^{\frac{m}{2}}\;f(u)$$ in a bounded domain of $\mathbf{R}^N$ with boundary $\partial\Omega$ of class $C^2$, $u|_{\partial\Omega}\;=\;+{\infty}$, $\omega\;\in\;L^{\infty}(\Omega)$, 0 < q < 1 and $a\;{\in}\;C^{\alpha}(\bar{\Omega})$, $\mathbf{R}^+$ is non-negative for some $\alpha\;\in$ (0,1), where $\mathbf{R}^+\;=\;[0,\;\infty)$. Under suitable growth assumptions on a, b and f, we show the exact blow-up rate and uniqueness of the large solutions. Our proof is based on the method of sub-supersolution.
Keywords
Large solutions; blow-up rate; uniqueness; sub-supersolutions;
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