具非线性边界条件的Volterra型时滞微分方程边值问题奇摄动

Abstract

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

CLC Number:

34K10

LIN Jing-Chi, GE Wei-Gao. Singularly Perturbed Boundary Value Problems for Volterra Retarded Differential Equations with Nonlinear Boundary Conditions[J].Acta mathematica scientia,Series A, 2003, 23(4): 504-512.

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

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