具非线性边界条件的泛函微分方程边值问题奇摄动(英文)

研究一类具非线性边界条件的泛函微分方程边值问题εx″( t) =f ( t,x( t) ,x( t-τ) ,x′( t) ,ε) ,　 t∈ ( 0 ,1 ) ,x( t) =φ( t,ε) ,　 t∈ -τ,0 ],　 h( x( 1 ) ,x′( 1 ) ,ε) =A(ε) .我们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 Functional Differential Equations with Nonlinear Boundary Conditions

A kind of boundary value problems for functional differential equations with nonlinear boundary condition as followsεx"(t)=f(t,x(t),x(t-τ),x'(t),ε),t∈(0,1),x(t)=ψ(t,ε),t∈-τ,0],h(x(1),x'(1),ε)=A(ε)is studied. Using 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.