Hostname: page-component-78c5997874-m6dg7 Total loading time: 0 Render date: 2024-11-10T13:37:28.881Z Has data issue: false hasContentIssue false
  • English
  • Français

Oscillation Criteria for Second Order Neutral Differential Equations

Published online by Cambridge University Press:  20 November 2018

Horng-Jaan Li  and
Wei-Ling Liu
Horng-Jaan Li
Affiliation:
Chienkuo Junior College of Technology and Commerce, Chang-Hua, Taiwan, Republic of China
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Some oscillation criteria are given for the second order neutral delay differential equation

where τ and σ are nonnegative constants, . These results generalize and improve some known results about both neutral and delay differential equations.

Keywords

34K1534C10
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 48 , Issue 4 , 01 August 1996 , pp. 871 - 886
Copyright
Copyright © Canadian Mathematical Society 1996

References

1. Grace, S.R. and Lalli, B.S., Oscillations of nonlinear second order neutral delay differential equations, Rat., Mat. 3(1987), 77–84.Google Scholar
2. Grammatikopoulos, M.K., Ladas, G. and Meimaridou, A., Oscillations of second order neutral delay differential equations, Rat., Mat. 1(1985), 267–274.Google Scholar
3. Hale, J.K., Theory of Functional Differential Equations, Springer- Verlag, New York, (1977).Google Scholar
4. Hartman, P., On nonoscillatory linear differential equations of second order, Amer. J., Math. 74(1952), 389–40.Google Scholar
5. Kamenev, I.V., Integral criterion for oscillation of linear differential equations of second order, Mat. Zametki (1978), 249–251.Google Scholar
6. Leighton, W., The detection of the oscillation of solutions of a second order linear differential equation, Duke Math., J. 17(1950), 57–61.Google Scholar
7. Moore, R.A., The behavior of solutions of a linear differential equation of second order, Pacific J., Math. 5(1955), 125–145.Google Scholar
8. Ruan, S., Oscillations of second order neutral differential equations, Canad. Math., Bull. 36(1993), 485–496.Google Scholar
9. Philos, Ch. G., Oscillation theorems for linear differential equations of second order, Arch., Math. 53(1989), 482–492.Google Scholar
10. Travis, C.C., Oscillation theorems for second order differential equations with functional arguments, Proc. Amer. Math., Soc. 31(1972), 199–202.Google Scholar
11. Waltman, P., A note on an oscillation criterion for an equation with a function argument, Canad. Math., Bull. 11(1968), 593–595.Google Scholar
12. Wintner, A., A criterion of oscillatory stability, Quart. Appl., Math. 7(1949), 115–117.Google Scholar
13. Wong, J.S., An oscillation criterion for second order nonlinear differential equations with iterated integral averages, Differential Integral, Equations 6(1993), 83–91.Google Scholar
14. Yan, J., Oscillation theorems for second order linear differential equations with damping, Proc. Amer. Math., Soc. 98(1986), 276–282.Google Scholar
15. Yu, Y.H., Leighton type oscillation criterion and Sturm type comparison theorem, Math., Nachr. 153(1991), 485–496.Google Scholar