Abstract: The asymptotic behaviours of the solutions to the nonlinear differential equation of the type with delays:y'(t)=f(t,y(t))+g(t,y(t)y(t-τ(t))∫_t0^th(t,s,y(s),y(s-τ(s)))as)t∈[t₀,∞]y∈R are studied.The main tools used here are new integral inequalitieg. The sufficient conditions on boundedness, stability and exponential asymptotic stability of the solutions are established.

Key words: integral inequalities, delay differential equation, boundedness, stability, exponential asymptotic stability

摘要： 我们利用为作者得到的一类新的积分不等式研究了如下的具时滞的微分方程:y'(t)=f(t,y(t))+g(t,y(t)y(t-τ(t))∫_t0^th(t,s,y(s),y(s-τ(s)))as)t∈[t₀,∞]y∈R得到了解的有界性、稳定性和指数渐近稳定性的充分条件。

关键词: 积分不等式, 时滞微分方程, 有界性, 稳定性, 指数渐近稳定性