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The purpose of this paper is two-fold; firstly, we shall derive some new results concerning a singular perturbation problem describing the stationary distribution of two competing and diffusing species; secondly, we want to demonstrate the power of a technique using approximate Green functions to prove the validity of a constructed formal approximation in a singular perturbation problem.

Approximate Green functions as a tool to prove correctness of a formal approximation in a model of competing and diffusing species