Philos, Christos G.; Purnaras, Ioannis K. Asymptotic properties, nonoscillation, and stability for scalar first order linear autonomous neutral delay differential equations. (English) Zbl 1054.34109 Electron. J. Differ. Equ. 2004, Paper No. 03, 17 p. (2004). The neutral delay differential equation \[ \frac {d}{dt} \left[ x(t)+\int_{-\sigma}^0x(t+s)d\zeta (s) \right]= \int_{-\tau}^0x(t+s)\,d\eta (s) \] is considered, where \(\sigma\), \(\tau\) are positive constants, \(\zeta\) and \(\eta\) are real-valued functions of bounded variation on the intervals \([-\sigma,0]\) and \([-\tau,0]\), respectively, and the integrals are Riemann-Stieltjes integrals. It is supposed that \(\eta\) is not constant on \([-\tau,0]\). New results on the asymptotic behavior (e.g., on the nonoscillation and the stability) of solutions are proved. Results are obtained via a real root (with an appropriate property) of the characteristic equation. Applications to the special case of delay differential equations are also presented. Reviewer: Josef DiblĂk (Brno) Cited in 11 Documents MSC: 34K11 Oscillation theory of functional-differential equations 34K20 Stability theory of functional-differential equations 34K25 Asymptotic theory of functional-differential equations 34K40 Neutral functional-differential equations Keywords:neutral differential equation; asymptotic behavior; nonoscillation; stability PDFBibTeX XMLCite \textit{C. G. Philos} and \textit{I. K. Purnaras}, Electron. J. Differ. Equ. 2004, Paper No. 03, 17 p. (2004; Zbl 1054.34109) Full Text: EuDML EMIS