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

This paper studies two-point boundary value problems for two-component systems with a small parameter ε. The boundary conditions are of Neumann type. First it is shown that the reduced problem (ε = 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 (ε > 0), which possess transition layers. As an application, a model system of prey-predator interaction with diffusion is considered.