| SINGULARLY PERTURBED BOUNDARY VALUE PROBLEMS FOR SEMI-LINEAR RETARDED DIFFERENTIAL EQUATIONS WITH NONLINEAR BOUNDARY CONDITIONS |
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| 作者姓名： | 任景莉 葛渭高 |
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| 作者单位： | Department of Mathematics，Beijing Institute of Technology，Department of Mathematics，Zhengzhou University Beijing 100081，P.R.China，Department of Mathematics，Zhengzhou University，Zhengzhou 450052，P.R.China，Zhengzhou 450052，P.R.China |
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| 基金项目： | theNationalNaturalScienceFoundationofChina (1 9871 0 0 5) |
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| 摘 要： | IntroductionInthispaper,westudiedakindofboundaryvalueproblems (BVPs)forsemi_linearretardeddifferentialequationwithnonlinearboundarycondition : εx″(t) =f(t,x(t) ,x(t-ε) ,ε) , t∈(0 ,1 ) ,(1 ) x(t) =φ(t,ε) , t∈-ε0 ,0 ] ,h(x(1 ) ,x′(1 ) ,ε) =A(ε) ,(2 )whereε>0isasmallparameterandε0 isasufficientlysmallpositiveconstant.ThereweremanyresultsofstudyingonsingularlyperturbedboundaryvalueproblemforretardeddifferentialequationinRefs.1～5] .Butthosestudiespossessedanesse…
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| 收稿时间： | 19 April 2001 |
Singularly perturbed boundary value problems for semi-linear retarded differential equations with nonlinear boundary conditions |
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| Jing-li,Ren,Wei-gao,Ge.SINGULARLY PERTURBED BOUNDARY VALUE PROBLEMS FOR SEMI-LINEAR RETARDED DIFFERENTIAL EQUATIONS WITH NONLINEAR BOUNDARY CONDITIONS[J].Applied Mathematics and Mechanics(English Edition),2003,24(12):1450-1455. |
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| Authors: | Jing-li Ren Wei-gao Ge |
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| Institution: | 1. Department of Mathematics, Beijing Institute of Technology, Beijing 100081, P.R. China;Department of Mathematics, Zhengzhou University, Zhengzhou 450052, P.R. China
2. Department of Mathematics, Beijing Institute of Technology, Beijing 100081, P.R. China |
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| Abstract: | A boundary value problems for functional differenatial equations, with nonlinear boundary condition, is studied by the theorem of differential inequality. Using new method to construct the upper solution and lower solution, sufficient conditions for the existence of the problems' solution are established. A uniformly valid asymptotic expansions of the solution is also given. |
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| Keywords: | singular perturbation functional differential equation boundary value problem uniformly valid asymptotic expansion |
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