一类时滞微分方程正解的存在性

Existence of Nonoscillation Solutions of a Delay Differential Equation

研究一类一阶非线性时滞微分方程,x(′t)+a(t)f(x(t))+p(t)g(x(t))h(x(t-1τ(t)),x(t-2τ(t)),…,x(t-nτ(t)))=0,其中,a,p,jτ∈C(R+,R+),limt→+∞(t-1τ(t))=+∞,j=1,2,…,n,f,g∈C(R,R),获得了其存在正解的充分条件.

In this paper we consider the first order nonlinear delay differential Equa- tion x′（t）＋a（r）f（x（t））＋p（t）g（x（t））h（x（t-τ1（t））,x（t-τ2（t））,…,x（t-τn（t）））=0,where a,p,τj∈C（R^＋,R^＋）,limt→＋∞（t-τ1（t））=＋∞,j=1,2,…,n,f,g∈C（R,R）,and a sufficient condition for the above equation existed positive solution is obtained.