具有“小”延迟的方程x′(t)=ax(t)+bx(t-τ)

Equation x′(t)=ax(t)+bx(t-τ) with Small-delay

以一个简单的例子简明地讨论了泛函微分方程的几个基本问题.例如解的存在性、惟一性、稳定性、渐进性态、常用解法,并指出有关的参考文献.特别是只用初等微积分证明了一个定理及它的几个推理,而且所求出的解的指数趋进的渐进值是新的.

In this paper, we discuss some basic problems of functional differential equation by using a simple example, such as the actual significance. The existence, the uniqueness, the stability, the asymptotic behavior of solutions and the usual solving methods. Especially we prove a theorem and its corollaries only by using elementary calculus. And the exponentially asymptotic value of the solution is new.