Multiple Solutions of Two-Point Boundary Value Problems of Neumann Type with a Small Parameter

Abstract

This paper studies two-point boundary value problems for two-component systems with a small parameter $\varepsilon $. The boundary conditions are of Neumann type. First it is shown that the reduced problem $(\varepsilon = 0)$ has multiple solutions. With the aid of this result, the singular perturbation method is used for constructing large amplitude solutions of the original problem $(\varepsilon > 0)$, which possess transition layers. As an application, a model system of prey-predator interaction with diffusion is considered.