Oscillations of delay differential equations with variable coefficients

E. Jagathprabhav; V. Dharmaiah

doi:10.26637/MJM0802/0028

Abstract

The purpose of this paper is to obtain a sharp sufficient condition for the oscillation of the delay differential equation
$y^{\prime}(x)+q(x) y(x-\tau)=0, \quad x \geq x_0,$
where $q(x) \in C\left(\left[x_0, \infty\right), R^{+}\right)$ which improves previously known results.

Keywords:

Delay differential equation, Oscillatory property

Mathematics Subject Classification:

Mathematics

Authors Imprint References Funding Related Articles Downloads

E. Jagathprabhav Department of Mathematics, Osmania University, Hyderabad-500007, India.
V. Dharmaiah Department of Mathematics, Osmania University, Hyderabad-500007, India.

Pages: 489-493
Date Published: 01-04-2020
Vol. 8 No. 02 (2020): Malaya Journal of Matematik (MJM)

G. Ladas, Sharp conditions for oscillations caused by delay, Appl. Anal., 9(1979), 93-98.

R. G. Koplatadze and T. A. Chanturia, On the oscillatory and monotone solutions of the first order differential equations with deviating arguments, Differentsial'nyeUravneniya, 18(1982), 1463-1465.

M. K. Grammatikopoulos, E. A. Grove, and G. Ladas, Oscillations of first-order neutral delay differential equations, J. Math. Anal. Appl., 120(1986), 510-520.

Q. Chuanxi and G. Ladas, Oscillations of neutral differential equations with variable coefficients, Appl. Anal., $32(1989), 215-228$.

${ }^{[5]}$ G. Ladas and C. Qian, Oscillation in differential equations with positive and negative coefficients, Canad. Math. Bull., 33(1990), 442-451.

I. Gyori and G. Ladas, Oscillation Theory of Delay Differential Equations with Applications, Clarendon, Oxford, 1991.

Bingtuan Li, Oscillations of delay differential equations with variable coefficients, J. Math. Anal. Appl., 192(1995), 312-321.

G. S. Ladde, V. Lakshmikantham, and B. G. Zhang, Oscillation Theory of Differential Equations with Deviating Arguments, Marcel Dekker, New York, 1987.