Oscillation of first order delay differential equations

Li, Bingtuan

doi:10.1090/S0002-9939-96-03674-X

Oscillation of first order delay differential equations
HTML articles powered by AMS MathViewer

by Bingtuan Li PDF

Proc. Amer. Math. Soc. 124 (1996), 3729-3737 Request permission

Abstract:

We introduce a new technique to analyze the generalized characteristic equations to obtain some infinite integral conditions for oscillation of the nonautonomous delay differential equations.

References

M. I. Tramov, Conditions for the oscillation of the solutions of first order differential equations with retarded argument, Izv. Vysš. Učebn. Zaved. Matematika 3(154) (1975), 92–96 (Russian). MR 0380060
Gerasimos Ladas, Sharp conditions for oscillations caused by delays, Applicable Anal. 9 (1979), no. 2, 93–98. MR 539534, DOI 10.1080/00036817908839256
R. G. Koplatadze and T. A. Chanturiya, Oscillating and monotone solutions of first-order differential equations with deviating argument, Differentsial′nye Uravneniya 18 (1982), no. 8, 1463–1465, 1472 (Russian). MR 671174
G. Ladas and I. P. Stavroulakis, Oscillations caused by several retarded and advanced arguments, J. Differential Equations 44 (1982), no. 1, 134–152. MR 651691, DOI 10.1016/0022-0396(82)90029-8
O. Arino, I. Győri, and A. Jawhari, Oscillation criteria in delay equations, J. Differential Equations 53 (1984), no. 1, 115–123. MR 747409, DOI 10.1016/0022-0396(84)90028-7
Brian R. Hunt and James A. Yorke, When all solutions of $x^{\prime } =-\sum q_{i}(t)x(t-T_{i}(t))$ oscillate, J. Differential Equations 53 (1984), no. 2, 139–145. MR 748236, DOI 10.1016/0022-0396(84)90036-6
M. K. Grammatikopoulos, E. A. Grove, and G. Ladas, Oscillations of first-order neutral delay differential equations, J. Math. Anal. Appl. 120 (1986), no. 2, 510–520. MR 864767, DOI 10.1016/0022-247X(86)90172-1
István Győri, Oscillation conditions in scalar linear delay differential equations, Bull. Austral. Math. Soc. 34 (1986), no. 1, 1–9. MR 847968, DOI 10.1017/S0004972700004457
G. S. Ladde, V. Lakshmikantham, and B. G. Zhang, Oscillation theory of differential equations with deviating arguments, Monographs and Textbooks in Pure and Applied Mathematics, vol. 110, Marcel Dekker, Inc., New York, 1987. MR 1017244
B. G. Zhang and K. Gopalsamy, Oscillation and nonoscillation in a nonautonomous delay-logistic equation, Quart. Appl. Math. 46 (1988), no. 2, 267–273. MR 950601, DOI 10.1090/S0033-569X-1988-0950601-7
G. Ladas and C. Qian, Oscillation in differential equations with positive and negative coefficients, Canad. Math. Bull. 33 (1990), no. 4, 442–451. MR 1091349, DOI 10.4153/CMB-1990-072-x
Yuan Ji Cheng, Oscillation in nonautonomous scalar differential equations with deviating arguments, Proc. Amer. Math. Soc. 110 (1990), no. 3, 711–719. MR 1023349, DOI 10.1090/S0002-9939-1990-1023349-4
I. Győri and G. Ladas, Oscillation theory of delay differential equations, Oxford Mathematical Monographs, The Clarendon Press, Oxford University Press, New York, 1991. With applications; Oxford Science Publications. MR 1168471
Man Kam Kwong, Oscillation of first-order delay equations, J. Math. Anal. Appl. 156 (1991), no. 1, 274–286. MR 1102611, DOI 10.1016/0022-247X(91)90396-H
G. Ladas, C. Qian, and J. Yan, A comparison result for the oscillation of delay differential equations, Proc. Amer. Math. Soc. 114 (1992), no. 4, 939–947. MR 1052575, DOI 10.1090/S0002-9939-1992-1052575-5
B. Li, Oscillations of delay differential equations with variable coefficients, J. Math. Anal. Appl. 192 (1995), 312–321.
L. H. Erbe, Qingkai Kong and B. G. Zhang, Oscillation theory for functional differential equations, Marcel Dekker, New York, 1995.