拟线性积分微分方程组边值问题的奇摄动

SINGULAR PERTURBATION OF BOUNDARY VALUE PROBLEM FOR THE QUASILINEAR INTEGRODIFFERENTIAL EQUATION SYSTEMS

本文研究奇摄动积分微分方程组边值问题：其中ε为正的小参数，Tx为定义在[0，1]上的积分算子，x、g、x0和x1为n维向量函数，f（t，ε）为n×n矩阵。在适当的条件下利用对角化方法证明了解的存在性，构造出解的渐近展开式并给出了余项的估计。

In this paper, the singular perturbation of boundary value problem for the quasilinear integro-differential equation systems：εx″=f（t,ε）x′＋g（t,x,Tx,ε） x（0,ε）=x^0（ε）, x（1,ε）=x^1（ε） is considered, where ε is a positive small parameter, Tx is integral operator defined in [0, 1], x,g,x^0 and x^1 are n-dimension vector functions, f（t, ε） is n×n matrix. Under the appro- priate assumptions, using the diagonalization method, the existence of solution is proved and a asymptotic expansion of the solution is constructed and the estimate of the remainder term is given.