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December 2012 Positive Solutions for Non-cooperative Singular $p$-Laplacian Systems
D. D. HAI
Tokyo J. Math. 35(2): 321-331 (December 2012). DOI: 10.3836/tjm/1358951321

Abstract

We prove the existence of\ positive solutions for the $p$-Laplacian system \[ \left\{ \begin{array}{@{\,}c@{\enskip}c} -\Delta _{p}u_{1}=\lambda f_{1}(u_{2}) &\text{in}~\Omega \,, \\ -\Delta _{p}u_{2}=\lambda f_{2}(u_{1}) &\text{in}~\Omega \,, \\ \ \ \ \quad u_{1}=u_{2}=0 & \text{on}~\partial \Omega \,, \end{array} \right. \] where $\Delta _{p}u=\mbox{div}(|\nabla u|^{p-2}\nabla u),p>1, \Omega$ is a bounded domain in $\mathbf{R}^{n}$ with smooth boundary $\partial \Omega ,f_{i}:(0,\infty) \rightarrow \mathbf{R}$ are possibly singular at 0 and are not required to be positive or nondecreasing, and $\lambda $ is a large parameter.

Citation

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D. D. HAI. "Positive Solutions for Non-cooperative Singular $p$-Laplacian Systems." Tokyo J. Math. 35 (2) 321 - 331, December 2012. https://doi.org/10.3836/tjm/1358951321

Information

Published: December 2012
First available in Project Euclid: 23 January 2013

zbMATH: 1279.35036
MathSciNet: MR3058709
Digital Object Identifier: 10.3836/tjm/1358951321

Subjects:
Primary: 35J25
Secondary: 35J70

Rights: Copyright © 2012 Publication Committee for the Tokyo Journal of Mathematics

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Vol.35 • No. 2 • December 2012
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