奇摄动半线性时滞微分方程边值问题

Singularly Perturbed Boundary Value Problems for Semilinear Differential Equations with Delay

本文研究半线性时滞微分方程边值问题εx″(t) =f (t,x(t) ,x(t-ε) ,ε) ,t∈ (0 ,1 ) ,x(t) =φ(t,ε) ,t∈ [-ε,0 ],x(1 ) =A(ε) .利用不动点原理及微分不等式理论 ,我们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, we study a kind of singularly perturbed boundary value problem for semilinear differential equations with delay [HL(2:1,Z;2,Z] εx″(t)=f(t,x(t),x(t-ε),ε),t∈(0,1), x(t)=φ(t,ε), t∈[-ε,0],x(1)=A(ε). Using the fixed point principle and the theory of differential inequality, we prove the existence of the solution and an uniformly valid asymptotic expansions of the solution is given as well.