一阶中立型线性微分差分方程的非振动解的类型及判别

Typies of Nonoscillatory Solutions of First Order Neutral Linear Differential-Difference Equation And Their Criteria

本文讨论一阶中立型线性微分差分方程其中,给出了方程(1)非振动解存在的类型,得到了方程(1)存在A_K型非振动解的充要条件和存在A_o型非振动解的充分条件.

In this paper, We consider the equationx’(t)-Cx’(t-r)+p(t)x(g(t)) = 0 ( 1 )where r>0, p(t)>0, 0≤C<1, g(t)≤t, lim g(t)=+∞ t→+ ∞We find the typies of nonoscillatory Solutions of equation(l). A suffici-nt and necessary condition for(l) existence of △K type nonoscillatory solu-tions and some sufficient conditions for(l) existence of A0 type nonoscilla-tory solutions are obtained.