zbMATH — the first resource for mathematics

Oscillation and nonoscillation of advanced differential equations with variable coefficients. (English) Zbl 1013.34067
The authors study the scalar advanced delay differential equations \(x'(t)-p(t)x(t+\tau)=0\) and \(x'(t)-\sum_{i=1}^n p_i(t) x(t+\tau_i)=0 \) with positive constants \(\tau,\tau_i\) and nonnegative continuous functions \(p, p_i\). Sharp sufficient conditions are shown for the oscillation and nonoscillation of the solutions. The results improve and extend the corresponding ones of G. Ladas and I. P. Stavroulakis [J. Differ. Equations 44, 134-152 (1982)].

34K11 Oscillation theory of functional-differential equations
PDF BibTeX Cite
Full Text: DOI
[1] Gyori; Ladas, G., Oscillation theory of delay differential equations with applications, (1991), Clarendon Oxford · Zbl 0780.34048
[2] Ladas, G., Sharp conditions for oscillations caused by delays, Appl. anal., 9, 93-98, (1979) · Zbl 0407.34055
[3] Ladde, G.S.; Lakshmikantham, V.; Zhang, B.G., Oscillation theory of differential equations with deviating arguments, (1987), Marcel Dekker New York · Zbl 0832.34071
[4] Li, B., Oscillations of delay differential equation with variable coefficients, J. math. anal. appl., 192, 312-321, (1995) · Zbl 0829.34060
[5] Ladas, G.; Stavroulakis, I.P., Oscillations caused by several retarded and advanced arguments, J. differential equations, 44, 134-152, (1982) · Zbl 0452.34058
[6] Kusano, T., On even order functional differential equation with advanced and retarded arguments, J. differential equations, 45, 75-84, (1982) · Zbl 0512.34059
[7] Kulenovic, M.R.; Grammatikopoulos, M.K., Some comparison and oscillation results for first order differential equations and inequalities with a deviating argument, J. math. anal. appl., 131, 67-84, (1988) · Zbl 0664.34071
[8] Koplatadze, R.G.; Chanturria, T.A., On the oscillatory and monotone solutions of the first order differential equations with deviating arguments, Differentsial’nye uravneniya, 18, 1463-1465, (1982) · Zbl 0496.34044
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.