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A unique positive solution to a system of semilinear elliptic equations

Pages: 193 - 195, Volume 2013, Issue special, November 2013      doi:10.3934/proc.2013.2013.193

 
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Diane Denny - Department of Mathematics and Statistics, Texas A&M University - Corpus Christi, Corpus Christi, Texas 78412, United States (email)

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 $\kappa>0$.

Keywords:  Elliptic, existence, uniqueness, semilinear.
Mathematics Subject Classification:  Primary: 35A02.

Received: July 2012;      Revised: November 2012;      Available Online: November 2013.

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