Article Contents
Article Contents

# A unique positive solution to a system of semilinear elliptic equations

• 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 $\kappa>0$.
Mathematics Subject Classification: Primary: 35A02.

 Citation:

•  [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.
Open Access Under a Creative Commons license