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

Applied Mathematics and Mechanics (English Edition) ›› 2003, Vol. 24 ›› Issue (12): 1441-1449.

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

鲁世平

Department of Mathematics, Anhui Normal University, Wuhu, Anhui 241000, P.R.China

收稿日期:2001-06-07 修回日期:2003-05-13 出版日期:2003-12-18 发布日期:2003-12-18
通讯作者: LIN Zong-chi,Original Member of Editorial Committee,AMM
基金资助:
the Natural Science Foundation of Education Department of Anhui Province of China(2002kj133)

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

LU Shi-ping

Department of Mathematics, Anhui Normal University, Wuhu, Anhui 241000, P.R.China

Received:2001-06-07 Revised:2003-05-13 Online:2003-12-18 Published:2003-12-18
Supported by:
the Natural Science Foundation of Education Department of Anhui Province of China(2002kj133)

摘要/Abstract

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.

Abstract: 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.

中图分类号:

O175.7

鲁世平. SINGULARLY PERTURBED NONLINEAR BOUNDARY VALUE PROBLEM FOR A KIND OF VOLTERRA TYPE FUNCTIONAL DIFFERENTIAL EQUATION[J]. Applied Mathematics and Mechanics (English Edition), 2003, 24(12): 1441-1449.

LU Shi-ping . SINGULARLY PERTURBED NONLINEAR BOUNDARY VALUE PROBLEM FOR A KIND OF VOLTERRA TYPE FUNCTIONAL DIFFERENTIAL EQUATION[J]. Applied Mathematics and Mechanics (English Edition), 2003, 24(12): 1441-1449.

参考文献

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

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

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