摘要
本文研究奇摄动积分微分方程的Robin边值问题 εy″=f(t,Ty,y,y′,ε), α(ε)y(0)—b(ε)y′(0)=A(ε),c(ε)y(1)+d(ε)y′(1)=B(ε),其中T是定义在C[0,1]上的一个积分算子。文中用微分不等式方法证明了解的存在性,构造出解的渐近展式并给出了余项的一致有效估计.最后把所得结果用于研究奇摄动四阶边值问题. εx^((4))=f(t,x,x″,x,ε), x(0)=φ(ε),x(1)=φ(ε), α(ε)x″(0)—b(ε)x(0)= A(ε),c(ε)x″(1)+d(ε)x(1)=B(ε).
The present paper covers the singularly perturbed Robin boundary value problems for the in-tegro-differential equation:εy' = f(t,Ty,y,g',ε),a(ε)y(0) - b(ε)y'(0) = A(ε), c(ε)y(1) + d(ε)y'(1) = B(ε),where T is an integral operator defined on C[0,1]. We first constructed a formal expansion of solution. Then we proved the existence of the solution and obtained the uniformly valid estimate of the remainder by the differential inequality technique. Finally we applied the results obtained above to the singularly perturbed boundary value problems for a fourth order ordinary differential equation.
出处
《吉林大学自然科学学报》
CAS
CSCD
1993年第1期7-16,共10页
Acta Scientiarum Naturalium Universitatis Jilinensis
基金
国家自然科学基金委资助课题
关键词
积分微分方程
边值问题
奇摄动
integro-differential equation, boundary value problem, singular perturbation
