Volteera型积分微分方程组边值问题的奇摄动

该文研究二阶积分微分方程组边值问题奇摄动，在适当的条件下，利用渐近分析方法和对角化技巧，还得解的存在性和给出解的渐近展开式与相应的余项估计．然后，应用这些结果到三阶常微分方程组边值问题的奇摄动，最后也得到解的一致有效的渐近展开式．

Singular Perturbation of Boundary Value Problem for System of Integro-Differential Equations

In this paper,considers the singular perturbation of boundary value problems forsecond order system of integro-differential equations. Under the suitable conditions the cxistence of the solution is proved and a asymptotic expansion of the solution and the estimation ofthe corresponding remainder term are geven by the asymptotic analysis method and the diagonalization technique. Then the results are applied to the singularly perturbed boundary valueproblem for the third order systems of ordinary differential equations. Finally a uniformly validasymptotic expansion of the solution is obtained as well.