特征根在虚轴上的奇摄动线性Neumann问题。非共振情况
Singularly perturbed linear Neumann problem with the characteristic roots on the imaginary axis. A non-resonant case
摘要：
本文研究非共振奇摄动线性Neumann边值问题\begin{eqnarray*} εy"+ky=f(t),\quad k>0,\quad 0<ε<<1,\quad t\in\langle a,b\rangle \end{eqnarray*} \begin{equation*} y'(a)=0,\quad y'(b)=0. \end{equation*}解的存在性和渐近性态。我们的方法是基于对等价于这个问题的一个积分方程的分析。
英文摘要：
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*} εy"+ky=f(t),\quad k>0,\quad 0<ε<<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.
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