具非线性边界条件的Volterra型时滞微分方程边值问题奇摄动  

Singularly Perturbed Boundary Value Problems for Volterra Retarded Differential Equations with Nonlinear Boundary Conditions

作　　者：任景莉[1] 葛渭高[1] 

机构地区：[1]北京理工大学数学系

出　　处：《数学物理学报（A辑）》2003年第4期504-512,共9页Acta Mathematica Scientia

基　　金：国家自然科学基金(198710 0 5);国家教育部高校博士点专项基金(1990 0 72 2 )资助

摘　　要：该文研究一类时滞微分方程边值问题εx″(t) =f(t,x(t) ,x(t-τ(t) ) ,[Tx] (t) ,x′(t) ,ε) ,t∈ (0 ,1 ) ,x(t) =φ(t,ε) ,t∈ [-τ,0 ] ,h(x(1 ) ,x′(1 ) ,ε) =A(ε) ,其中ε>0为小参数 ,τ(t)≥τ0 >0 ,τ=maxt∈ [0 ,1 ] τ(t) <1 ,[Tx] (t) =ψ(t) +∫t0 k(t,x) x(s) ds为Volterra型算子 .利用微分不等式理论证明了边值问题解的存在性 ,并给出了解的一致有效渐近展开式 .In this paper, the authors study a kind of boundary value problems for functional differential equations with nonlinear boundary conditionsεx″(t)=f(t,x(t),x(t-τ(t)),\(t),x′(t),ε),t∈(0,1), x(t)=φ(t,ε),t∈\,h(x(1),x′(1),ε)=A(ε),where ε>0 is a small parameter, τ(t)≥τ\-0>0,τ=\%\{max\}\%t∈\τ(t)<1,\(t)=ψ(t)+∫\+t\-0k(t,x)x(s) d s is a type of Volterra map. By using the theory of differential inequality, we prove the existence of the solution and uniformly valid asymptotic expansions of the solution is given as well.

关 键 词：奇摄动 时滞微分方程 边值问题 

分 类 号：O175.7[理学—数学]