Positive solutions of $p$-Laplacian equations withnonlinear boundary condition

Zuodong Yang; Jing Mo; Subei Li

doi:10.3934/dcdsb.2011.16.623

Article Contents

2011, Volume 16, Issue 2: 623-636. Doi: 10.3934/dcdsb.2011.16.623

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

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

Received: October 31, 2009

Revised: January 31, 2011

Published: August 2011

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Abstract

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.

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Mathematics Subject Classification: Primary: 35J65, 35J50; Secondary: 35J55.

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