Non-Resonant Non-Hyperbolic Singularly Perturbed Neumann Problem

Abstract

In this brief note, we study the problem of asymptotic behavior of the solutions for non-resonant, singularly perturbed linear Neumann boundary value problems εy″+ky=f(t), y′(a)=0, y′(b)=0, k>0, with an indication of possible extension to more complex cases. Our approach is based on the analysis of an integral equation associated with this problem.

Keywords

• singular perturbation
• linear ordinary differential equation
• Neumann boundary value problem