具有小时滞非自治线性中立型方程解的渐近性态  

ASYMPTOTIC BEHAVIOR OF THE SOLUTIONS OF THE NONAUTONOMOUS LINEAR NEUTRAL FUNCTIONAL DIFFERENTIAL EQUATIONS WITH SMALL DELAYS

作　　者：韦忠礼[1] 

机构地区：[1]山东建筑工程学院

出　　处：《高校应用数学学报（A辑）》1990年第4期575-586,共12页Applied Mathematics A Journal of Chinese Universities(Ser.A)

摘　　要：本文利用中立型方程解的可微性,研究了具有小时滞非自治线性中立型方程 d/(dt)D(t,x_t)=f(t,x_t)(*)解的渐近性态,即:x(t,t_0,φ)=Y(t,t_0)(l(φ)+o(1)),t→+∞,其中,D、f:R×C=R×C([-r,0],R^n)→R^n(r>0充分小)线性连续,x(t,t_0,φ)为方程(*)过(t_0,φ)∈S(R×C)的解,l是由φ确定的某向量,Y(t,t_0)是特解矩阵。This paper we use the differential property of the solutions of the neutral functional differential equations to study the asymptotic behavior of the solutions of the nonautono-mous linear neutral functional differential equationsd/dtD(t,xt)=f(t,xt) with small delays, i.e.:x(t,t0,φ)=Y(t,t0)(ι(φ)=o(1)),t→+∞Where D.f: R×C→Rn are linear on C, and are continuous on R×C, x(t, t0,φ) is a solution of (++) through (t0,φ) ∈S-(R×C),l is a vector- valued function on φ,Y(t,t,t0) is a special matrix solution.

关 键 词：中立型方程 解 渐近性态 线性 时滞 

分 类 号：O175[理学—数学]