On the 3/2 stability theorem for one-dimensional delay-differential equations
Consider the one-dimensional delay-differential equation (1) \(\dot x(t)=- a(t)x(t-\gamma (t))\) where a: [0,\(\infty)\to [0,\infty)\) and \(r: [0,\infty)\to [0,q].\) \textit{J. C. Lillo} [J. Differ. Equations 6, 1-35 (1969; Zbl 0174.398)] proved that if there is \(\alpha >0\) such that a(t)\(\leq \alpha\) and \(\alpha\) \(q\leq 3/2\), then the zero solution of (1) is uniformly stable. Furthermore, the upper bound 3/2 is the best possible for (1). In this paper the author considers such a problem for more general one-dimensional delay-differential equation than (1): (2) \(\dot x(t)=F(t,x_ t)\). He obtains some results on the uniform stability of the zero solution of (2).
scientific article; zbMATH DE number 4069388
scientific article