一类非线性中立型泛函微分方程解的稳定性

STABILITY OF SOLUTION TO A CLASS OF FUNCTIONAL DIFERENTIAL EQUATIONS OF NEUTRAL TYPE

研究了一类具有非线性算子 D(t,■)的中立型泛函微分方程(d/dt)D(t,x_i)=f(t,x_■). (E)首先,在适当条件下给出差分方程 D(t,y_■)=h(t)的解的渐近表达式,从而给出了非线性 D(t,■)算子一致稳定的充分条件.其次,应用 Liapunov 泛函方法给出方程(E)平凡解一致渐近稳定的结果,从本质上解决了一类具有非线性算子 D(t,(?))的中立型泛函微分方程解的稳定性问题.

A class of functional differential equations of neutial type with nonlinear difference op-erator D(t,■)(d/dt)D(t,x_t)=f(t,x_t)(E)is studied.First,under the proper conditions a asymptotic estimation of the solutions to thedifference equations D(t,y_t)=h(t)is established.A sufficient condition is given underwhich the nonlinear difference operator D(t,■)is uniformly stable.Second,a result on uni-formly asymptotic stability of the trivial solution to the equation(E)is obtained.The stabili-ty problem of the solutions to equations(E)with nonlinear difference operator is resolved es-sentially.