A comparison result for the oscillation of delay differential equations

Ladas, G.; Qian, C.; Yan, J.

doi:10.1090/S0002-9939-1992-1052575-5

A comparison result for the oscillation of delay differential equations
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by G. Ladas, C. Qian and J. Yan PDF

Proc. Amer. Math. Soc. 114 (1992), 939-947 Request permission

Abstract:

We obtain a comparison result for the oscillation of all solutions of the equation \[ \dot y(t) + \sum \limits _{i = 1}^n {{q_i}(t)y(t - {\sigma _i}(t)) = 0} \] in terms of the oscillation of all solutions of the equation \[ \dot x(t) + \sum \limits _{i = 1}^n {{p_i}(t)x(t - {\tau _i}(t)) = 0} \] under appropriate hypotheses on the asymptotic behavior of the quotients ${p_i}(t)/{q_i}(t)$ and ${\tau _i}(t)/{\sigma _i}(t)$ for $i = 1,2, \ldots ,n$. An application to the oscillation of the nonautonomous delay-logistic equation is given.

References

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
Jack Hale, Theory of functional differential equations, 2nd ed., Applied Mathematical Sciences, Vol. 3, Springer-Verlag, New York-Heidelberg, 1977. MR 0508721

On oscillatory and monotonous solutions of first order differential equation with deviating argument

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M. R. S. Kulenović, G. Ladas, and A. Meimaridou, On oscillation of nonlinear delay differential equations, Quart. Appl. Math. 45 (1987), no. 1, 155–164. MR 885177, DOI 10.1090/S0033-569X-1987-0885177-5
Man Kam Kwong and William T. Patula, Comparison theorems for first order linear delay equations, J. Differential Equations 70 (1987), no. 2, 275–292. MR 917624, DOI 10.1016/0022-0396(87)90165-3
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