A Singular Singularly Perturbed Nonlinear Vector Boundary Value Problem

In this paper, we are concerned with the question of singular perturbations to boundary value problems for the vector system dxdt = U(t, x, y, ϵ)ϵ2dxdt = V(t, x, ϵ2y, ϵ) as ϵ → 0+ by the method of constructing the formal asymptotic solution. Under some suitable assumptions, we prove the existence and local uniqueness of the perturbed solution and show that the formal asymptotic solution is the uniformly