Furumochi, Tetsuo; Hayashi, Akifumi Stability and oscillation in delay differential equations with piecewise constant arguments. (English) Zbl 0729.34056 Mem. Fac. Sci., Shimane Univ. 24, 21-30 (1990). The authors consider a first order nonlinear delay differential equation with piecewise constant arguments and obtain results on the asymptotic behaviour of solutions of the equation. Razumikhin type methods are employed to study the stability of the zero solution of the equation. The results are illustrated by appropriate examples. Reviewer: V.Sree Hari Rao (Hyderabad) MSC: 34K20 Stability theory of functional-differential equations 34C10 Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations 34D20 Stability of solutions to ordinary differential equations 34K99 Functional-differential equations (including equations with delayed, advanced or state-dependent argument) Keywords:first order nonlinear delay differential equation with piecewise constant arguments; asymptotic behaviour; Razumikhin type methods; stability PDFBibTeX XMLCite \textit{T. Furumochi} and \textit{A. Hayashi}, Mem. Fac. Sci., Shimane Univ. 24, 21--30 (1990; Zbl 0729.34056)