Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
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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)
  • Published : 2010.01.30
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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

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