×

The 3/2 stability theorem for one-dimensional delay-differential equations with unbounded delay. (English) Zbl 0755.34074

Conditions for uniform stability and uniform asymptotic stability are derived for equations of the type \(x'(t)=-a(t)x(g(t))\). The main assumptions are that \(g(t)\to\infty\) as \(t\to\infty\) and \(\sup_{t\geq 0}A(t)\leq 3/2\), \(\inf_{t\geq 0}A(t)>0\), where \(A(t)=\int^ t_{g(t)}a(s)ds\).

MSC:

34K20 Stability theory of functional-differential equations
34D20 Stability of solutions to ordinary differential equations
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] T. Hara, T. Yoneyama, and R. MiyazakiFunkcial. Ekvac.; T. Hara, T. Yoneyama, and R. MiyazakiFunkcial. Ekvac. · Zbl 0770.34051
[2] Yoneyama, T., On the \(32\) stability theorem for one-dimensional delay-differential equations, J. Math. Anal. Appl., 125, 161-173 (1987) · Zbl 0655.34062
[3] Yorke, J. A., Asymptotic stability for one dimensional differential-delay equations, J. Differential Equations, 7, 189-202 (1970) · Zbl 0184.12401
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.