Voulov, H. D.; Bainov, D. D. Nonuniform stability for a nonautonomous differential equation with “maxima”. (English) Zbl 0788.34076 Rend. Semin. Fac. Sci. Univ. Cagliari 62, No. 2, 101-113 (1992). The function \(\overline x:(-\infty,a) \to R\), \(\sigma<a\), is a solution of the initial value problem for the differential equation with maxima (1) \(x'(t)=f(t, \max_{g(t) \leq s \leq t} x(s))\), (2) \(x_ \sigma=\varphi \in E\) if \(\overline x \in C[\sigma,a)\), \(\overline x_ \sigma=\varphi\) and \(\overline x\) satisfies (1) for \(t \in[\sigma,a)\). \(E\) is a linear space of functions defined on \((-\infty,0]\) with certain properties which is supplied with a seminorm. In the paper several sufficient conditions are given which guarantee the stability of the zero solution to (1) and a necessary and sufficient condition is established for the uniform stability of that solution. Reviewer: W.Šeda (Bratislava) Cited in 3 Documents MSC: 34K20 Stability theory of functional-differential equations Keywords:initial value problem; differential equation with maxima; stability; uniform stability PDFBibTeX XMLCite \textit{H. D. Voulov} and \textit{D. D. Bainov}, Rend. Semin. Fac. Sci. Univ. Cagliari 62, No. 2, 101--113 (1992; Zbl 0788.34076)