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2006 Positive solution of Laplacian noncooperative system with potential control
M. Bezzarga, Khaled Kefi
Differential Integral Equations 19(9): 1019-1034 (2006).

Abstract

We are concerned with the uniform positivity preserving property on a domain $D$ of $\mathbb{R}^d$ ($d\geq 3$), for the noncooperative system \begin{equation}\label{sy} \left\{ \begin{array}{cccc} -\Delta u & = & f(.,u)-\mu av & \text{in } D, \\ -\Delta v & = & bu & \text{in }D, \\ \underset{ x \rightarrow \partial_{\infty} D }{\lim }u(x) & = & \underset{ x \rightarrow \partial_{\infty} D}{\lim }v(x) & = 0, \end{array} \right. \end{equation} where $\partial_{\infty}D=\left\{ \begin{array}{ccc} \partial D ,\ \ \mbox{if D is bounded},\\ \partial D\cup \{+\infty\}, \ \ \mbox{if not}. \end{array} \right.$ We give appropriate conditions on $a$, $b$ and $f$ to get the existence and positivity of the solutions with potential control.

Citation

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M. Bezzarga. Khaled Kefi. "Positive solution of Laplacian noncooperative system with potential control." Differential Integral Equations 19 (9) 1019 - 1034, 2006.

Information

Published: 2006
First available in Project Euclid: 21 December 2012

zbMATH: 1210.35077
MathSciNet: MR2262094

Subjects:
Primary: 35J55
Secondary: 35B05

Rights: Copyright © 2006 Khayyam Publishing, Inc.

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Vol.19 • No. 9 • 2006
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