Singular Perturbation of Boundary Value Problem for System of Integro-Differential Equations
You Zhefeng; Lin Zongchi(Department of Mathematics, Fujian Normal University, Fuchou, 350007)
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.