Abstract
In this article a system of semilinear elliptic partial differential equations is studied. This system determines the equilibria of the Volterra-Lotka equations describing prey-predator interactions with diffusion. To analyze the system, a new monotone scheme is presented. A rigorous foundation is given for numerical calculations by adapting a suitable finite difference method to the new monotone scheme. Earlier theories in finite differences are not successful in solving the system without this scheme.
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