A singular perturbation result and its application to mathematical ecology

Li, Lige; Ramm, A. G.

doi:10.1090/S0002-9939-1991-1043414-6

A singular perturbation result and its application to mathematical ecology
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Proc. Amer. Math. Soc. 111 (1991), 1043-1050 Request permission

Abstract:

Conditions are given for the solutions of the equation $\varepsilon Au = F(u)$ to converge to the solution of the limit nonlinear equation $F(u) = 0$ as $\varepsilon \to 0$. Applications to existence and uniqueness of the positive solutions of an elliptic predator-prey system are given.

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