Singularly perturbed linear Neumann problem with the characteristic roots on the imaginary axis. A non-resonant case

Abstract

In this note we are dealing with the problem of existence and asymptotic behavior of solutions for the non-resonant singularly perturbed linear Neumann boundary value problem \begin{eqnarray*} \epsilon y"+ky=f(t),\quad k>0,\quad 0<\epsilon<<1,\quad t\in\langle a,b\rangle \end{eqnarray*} \begin{equation*} y'(a)=0,\quad y'(b)=0. \end{equation*} Our approach is based on the analysis of an integral equation equivalent to this problem.