Singular Perturbations for a Class of Fourth-order Nonlinear Boundary Value Problem

This paper is devoted to study the following the singularly perturbed fourth-order ordinary differential equation ∈y(4) =f(t,y',y'',y'''),0t1,0e1 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.