Singular perturbation of boundary value problem of systems for quasilinear ordinary differential equations

In this paper, we study the singular perturbation of boundary value problem of systems for quasilinear ordinary differential equations: where xf. y ,h,A,B and C belong to Rn and a is a diagonal matrix. Under the appropriate assumptions, using the technique of diagonalization and the theory of differential inequalities we obtain the existence of solution and its componentwise uniformly valid asymptotic estimation.