The singularly perturbed problem of vector integro-differential equations

The singularly perturbed boundary value problem of scalar integro-differential equations has been studied extensively by the differential inequality method. However, it does not seem possible to carry this method over to a corresponding nonlinear vector integro-differential equation. Therefore, for n-dimensional vector integro-differential equations the problem has not been solved fully. Here, we study this nonlinear vector problem and obtain some results. The approach in this paper is to transform the appropriate integro-differential equations into a canonical or diagonalized system of two first-order equations.