关键词: singular perturbation, nonlinear boundary value problem, di?erential inequality;
 asymptotic expansion

Abstract: This paper is devoted to study the following the singularly perturbed fourth-order ordinary differential equation ∈y⁽⁴⁾ =f(t,y’,y’’,y’’’),0<t<1,0<ε<<1 with the nonlinear boundary conditions y(0)=y’(1)=0,p(y’’(0),y’’’(0))=0,q(y’’(1),y’’’(1))=0 where f:[0,1]×R3→R is continuous,p,q:R2→R are continuous. Under certain conditions, by introducing an appropriate stretching transformation and constructing boundary layer corrective terms, an asymptotic expansion for the solution of the problem is obtained. And then the uniformly validity of solution is proved by using the differential inequalities. 

Key words: singular perturbation, nonlinear boundary value problem, di?erential inequality;
 asymptotic expansion