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September  2011, 16(2): 623-636. doi: 10.3934/dcdsb.2011.16.623

## Positive solutions of $p$-Laplacian equations with nonlinear boundary condition

 1 Institute of Mathematics, School of Mathematics Science, Nanjing Normal University, Jiangsu Nanjing 210046, China, China 2 School of Mathematics and Physics, Xuzhou Institute of Technology, Xuzhou, Jiangsu 221111, China

Received  November 2009 Revised  February 2011 Published  June 2011

In this paper we study the following problem $-\triangle_{p}u+|u|^{p-2}u=f(x,u)$ in a bounded smooth domain $\Omega \subset {\bf R}^{N}$ with a nonlinear boundary value condition $|\nabla u|^{p-2}\frac{\partial u}{\partial\nu}=g(x,u)$. Results on the existence of positive solutions are obtained by the sub-supersolution method and the Mountain Pass Lemma.
Citation: Zuodong Yang, Jing Mo, Subei Li. Positive solutions of $p$-Laplacian equations with nonlinear boundary condition. Discrete & Continuous Dynamical Systems - B, 2011, 16 (2) : 623-636. doi: 10.3934/dcdsb.2011.16.623
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