THE ASYMPTOTIC EXPANSIONS OF SINGULARLY PERTURBED BOUNDARY VALUE PROBLEMS

In this paper we study the singularly perturbed boundary value problem:εy″=f(t,y,ε),y(0)=ξ(ε),y(1)=η(ε).where εis a positive small parameter.In the conditions:f(0,y,0)≥m,f(l,y,0)≥mand ff(t,y,ε)≥0 ,we prove the existences,and uniformly valid asymptotic expansions of solutions for the given boundary value problems,and hence we improve the existing results.