一类高阶非线性积分微分方程边值问题的奇摄动

SINGULARLY PERTURBED BOUNDARY VALUE PROBLEMS FOR A KIND OF THE HIGHER ORDER NONLINEAR INTEGRAL DIFFERENTIAL EQUATIONS

本文讨论了奇摄动积分微分方程εy^((n))(x)=f(x,Ty,y,y′,…,y^((n-2)),ε)的两点边值问题,其中ε>0是小参数,T为Volterra型积分算子。利用构造上下解的方法,证明解的存在定理,并给出解的渐近估计。

In this paper,we study the singularly perturbed two-point boundary value problems of integral differential equations: εy((n))=f(x,Ty,y,y^1,…,y^((n-2)),ε). Where ε>0 is a small parameter;T is a Volterra integai operator.Using the method of constructing the upper and lower solutions,we prove the existence theorem and give a estimation of the solution.