A unique positive solution to a system of semilinear ellipticequations

Diane Denny

doi:10.3934/proc.2013.2013.193

Article Contents

2013, Volume 2013: 193-195. Doi: 10.3934/proc.2013.2013.193 open access

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A unique positive solution to a system of semilinear elliptic equations

Diane Denny^1,

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

Received: June 30, 2012

Revised: October 31, 2012

Published: October 2013

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Abstract

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 $\kappa>0$.

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Mathematics Subject Classification: Primary: 35A02.

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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), 331-364.
[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), 759-778.
[3]	W. Zhou and X. Wei, Uniqueness of positive solutions for an elliptic system, Electronic Journal of Differential Equations, 2011 (2011), 1-6.