关键词: 奇摄动； , 时滞微分方程； , 边值问题

Abstract:

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.

Key words: Singular perturbation； , Retarded differential equations；  , Boundary value prob lem