具非线性边界条件的Volterra型时滞微分方程边值问题奇摄动

该文研究一类时滞微分方程边值问题〖JB({〗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),JB)]其中ε>0为小参数，τ(t)≥τ\-0>0,τ=\%\{max\}\%DD(X]t∈\0,1\]DD)]τ(t)<1,\Tx\](t)=ψ(t)+∫\+t\-0k(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。

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

In this paper, the authors study a kind of boundary value problems for functional differential equations with nonlinear boundary conditions〖JB({〗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),JB)]where ε>0 is a small parameter,  τ(t)≥τ\-0>0,τ=\%\{max\}\%DD(X]t∈\0,1\]DD)]τ(t)<1,\Tx\](t)=ψ(t)+∫\+t\-0k(t,x)x(s)ds is a type of Volterra map. By using the t heory  of differential inequality, we prove the existence of the solution and uniforml y valid asymptotic expansions of the solution is given as well.