【摘要】 本文考虑如下积分微分方程边值问题: εx″=f（t,x,T_εx,ε）x′+g（t,x,T_εx,ε）, x（0,ε）=A（ε）,x（1,ε）=B（ε）,其中ε>0是小参数,〔T_εx〕（t,ε）=φ（t,ε）+integral from n=0 to t （K（t, s）x（s,ε）ds）,K（t,s）≥0是〔0,1〕×〔0,1〕上的连续函数,φ（t,ε）是〔0,1〕×〔0,ε₀〕上关于ε的无穷次连续可微函数。在适当的假设下,利用复合展开法和微分不等式技巧,我们获得所述问题的解的存在性和高阶渐近估计。更多还原

【Abstract】 Abstract This paper concerns with the following boundary value problems of the integral-differential equations: εx″. = f（t, x, T_εx, ε）x′ + g （t, x, T_εx, ε）, x（0, ε） = A（ε）, x（1, ε）=B（ε）, where ε>0 is a small parameter, and [T_εx]（t, ε）=ψ（t, ε） + integral from n=0 to t K（t, s）x（s, ε）ds, K（t, s）≥0 is continuous on, [0, 1] x ψ（t, ε） is arbitrary order continuous differentiable with respect to ε on [0, 1]×[0, ε₀]. Under the pro- per assumptions, using the method of composite expand and the differential inequalities theory, we obtain the existence and a higher order approximation of the solution.更多还原