具有逐段常值变元逻辑方程的振动性

随着科学技术的发展,泛函微分方程与众多科学领域的研究结合得愈来愈紧密,例如,连续体力学、种群生态学、电力学、自动控制、经济数学等等.而客观世界中的许多现象都要用泛函微分方程作为它们的数学模型,因此研究它具有明确的理论意义和现实意义.该文讨论了具有逐段常值变元的逻辑方程N′(t)=N(t)(a+bN~p(t-l)-cN~q(t-l)+dN~p([t-k])-fN~q([t-k]))的振动性,对已有的结果作了推广,并且获得了振动的充分必要条件.

Scillations of Logistic Equations with Piecewise Constant Arguments

With the development of science and technology,functional differential equation gradually combined closely with many researches in different fields,such as,continuous mechanics,community ecology,electricity,automatic control,economic mathematical and so on.As many phenomenon in world can be translated into functional differential equation and solved with it,it definitely has significance both in theory and reality. This paper discusses the oscillation of the following logistic equations with piecewise constant arguments. N′(t)=N(t)(a+bN~p(t -l)-cN~q(t-l)+dN~p([t - k])-fN~q([t - k])) We extend the results in some literatures and obtain some necessary and sufficient conditions for the oscillation of the above logistic equations with piecewise constant arguments.