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 conditionsεx″(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.
出处
《数学物理学报（A辑）》
CSCD
北大核心
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
关键词
奇摄动
时滞微分方程
边值问题
Singular perturbation
Retarded differential equations
Boundary value problem.
