A unique positive solution to a system of semilinear elliptic equations

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2013, 2013(special): 193-195. doi: 10.3934/proc.2013.2013.193

A unique positive solution to a system of semilinear elliptic equations

1.	Department of Mathematics and Statistics, Texas A&M University - Corpus Christi, Corpus Christi, Texas 78412, United States

Received July 2012 Revised November 2012 Published November 2013

Abstract
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We study a system of semilinear elliptic equations that arises from a predator-prey model. Previous related work proved the existence of a unique positive solution to this system of equations in the special case in which the parameter $\alpha=0$ in this system of equations, provided that a positive parameter $\kappa$ in this system of equations is sufficiently large. We prove the existence of a unique positive solution to this system of equations for any $\alpha \geq 0$ and for any $\kappa>0$.

Keywords: uniqueness, existence, Elliptic, semilinear..

Mathematics Subject Classification: Primary: 35A0.

Citation: Diane Denny. A unique positive solution to a system of semilinear elliptic equations. Conference Publications, 2013, 2013 (special) : 193-195. doi: 10.3934/proc.2013.2013.193

References:

[1]	Y.H. Du and S.B. Hsu, A diffusive predator-prey model in heterogeneous environment,, Journal of Differential Equations, 203 (2004), 331. Google Scholar
[2]	Y.H. Du and M.X. Wang, Asymptotic behaviour of positive steady states to a predator-prey model,, Proceedings of the Royal Society of Edinburgh, 136A (2006), 759. Google Scholar
[3]	W. Zhou and X. Wei, Uniqueness of positive solutions for an elliptic system,, Electronic Journal of Differential Equations, 2011 (2011), 1. Google Scholar

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References:

[1]	Y.H. Du and S.B. Hsu, A diffusive predator-prey model in heterogeneous environment,, Journal of Differential Equations, 203 (2004), 331. Google Scholar
[2]	Y.H. Du and M.X. Wang, Asymptotic behaviour of positive steady states to a predator-prey model,, Proceedings of the Royal Society of Edinburgh, 136A (2006), 759. Google Scholar
[3]	W. Zhou and X. Wei, Uniqueness of positive solutions for an elliptic system,, Electronic Journal of Differential Equations, 2011 (2011), 1. Google Scholar

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