SINGULARLY PERTURBED NONLINEAR BOUNDARY VALUE PROBLEM FOR A KIND OF VOLTERRA TYPE FUNCTIONAL DIFFERENTIAL EQUATION  

作　　者：鲁世平 

机构地区：[1]Department of Mathematics, Anhui Normal University

出　　处：《Applied Mathematics and Mechanics(English Edition)》2003年第12期1441-1449,共9页应用数学和力学（英文版）

基　　金：theNaturalScienceFoundationofEducationDepartmentofAnhuiProvinceofChina (2 0 0 2kj1 3 3 )

摘　　要：By employing the theory of differential inequality and some analysis methods, a nonlinear boundary value problem subject to a general kind of second_order Volterra functional differential equation was considered first. Then, by constructing the right_side layer function and the outer solution, a nonlinear boundary value problem subject to a kind of second_order Volterra functional differential equation with a small parameter was studied further. By using the differential mean value theorem and the technique of upper and lower solution, a new result on the existence of the solutions to the boundary value problem is obtained, and a uniformly valid asymptotic expansions of the solution is given as well.By employing the theory of differential inequality and some analysis methods, a nonlinear boundary value problem subject to a general kind of second_order Volterra functional differential equation was considered first. Then, by constructing the right_side layer function and the outer solution, a nonlinear boundary value problem subject to a kind of second_order Volterra functional differential equation with a small parameter was studied further. By using the differential mean value theorem and the technique of upper and lower solution, a new result on the existence of the solutions to the boundary value problem is obtained, and a uniformly valid asymptotic expansions of the solution is given as well.

关 键 词：singular perturbation functional differential equation boundary value problem uniformly valid asymptotic expansion 

分 类 号：O175.7[理学—数学]