Oscillation of nonlinear second order neutral delay dynamic equations on time scales
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In this paper, we establish some oscillation criteria for nonau-tonomous second order neutral delay dynamic equations(x(t) ± r(t)x(γ(t)))ΔΔ + H (t,x(h₁(t)),xΔ (h₂(t))) = 0 on a time scale T. Oscillatory behavior of such equations is not studiedbefore. This is a rst paper concerning these equations. The resultsare not only can be applied on neutral dierential equations when T =R, neutral delay dierence equations when T = N and for neutral delayq dierence equations when T = qN for q > 1, but also improved mostprevious results. Finally, we give some examples to illustrate our mainresults. These examples are not discussed before and there is no previoustheorems determine the oscillatory behavior of such equations.
Abstract
In this paper, we establish some oscillation criteria for nonau-tonomous second order neutral delay dynamic equations(x(t) ± r(t)x(γ(t)))ΔΔ + H (t,x(h₁(t)),xΔ (h₂(t))) = 0 on a time scale T. Oscillatory behavior of such equations is not studiedbefore. This is a rst paper concerning these equations. The resultsare not only can be applied on neutral dierential equations when T =R, neutral delay dierence equations when T = N and for neutral delayq dierence equations when T = qN for q > 1, but also improved mostprevious results. Finally, we give some examples to illustrate our mainresults. These examples are not discussed before and there is no previoustheorems determine the oscillatory behavior of such equations.
참고문헌 (17)
- R. P. Agarwal, "Oscillation criteria for second-order nonlinear neutral delay dynamic equations", J. Math. Anal. Appl, 300(1), pp.203~217 (2004)
- H. A. Agwo, "On the oscillation of second order neutral delay dynamic equations with several delays and variable coefficients", Int. J. Appl. Math. Stat, 5(S06), pp.65~73 (2006)
- H. A. Agwo, "On the oscillation of second order nonlinear neutral delay dynamic equations", ~
- E. Akin-Bohner, "Oscillation criteria for a certain class of second order Emden-Fowler dynamic equations", Electronic Transaction of Numerical Anal
- M. Bohner, "Oscillation for nonlinear second-order dynamic equations on a time scale", J. Math. Anal. Appl, 301(2), pp.491~507 (2005)
- M. Bohner, "Advances in Dynamic Equations on Time Scales" (2003), Birkh¨auser
- M. Bohner, "Dynamic Equations on Time Scales: An Introduction with Application" (2001), Birkh¨auser
- L. Erbe, "Kamenev-type oscillation criteria for secondorder linear delay dynamic equations", Dynam. Systems Appl, 15(1), pp.65~68 (2006)
- I. Gy¨ori, "Oscillation Theory of Delay Differential Equations, With applications. Oxford Mathematical Monographs" (1991), Oxford Science Publications. The Clarendon Press, Oxford University Press
- S. Hilger, "Analysis on measure chains— unified approach to continuous and discrete calculus", Results Math, 18(1), pp.18~26 (1990)
- J. Jiang, "Oscillation of second order nonlinear neutral differential equations", Appl. Math. Comput, 135(2), pp.531~540 (2003)
- G. S. Ladde, "Oscillation Theory of Differential Equations with Deviating Arguments, Monographs and Textbooks in Pure and Applied Mathematics, 110" (1987), Marcel Dekker, Inc.
- X. Lin, "Oscillation of second-order nonlinear neutral differential equations", J. Math. Anal. Appl, 309(2), pp.442~452 (2005)
- Y. S¸ahiner, "On oscillation of second order neutral type delay differential equations", Appl. Math. Comput, 150(3), pp.697~706 (2004)
- S. H. Saker, "Oscillation of second-order nonlinear neutral delay dynamic equations on time scales", J. Comput. Appl. Math, 187(2), pp.123~141 (2006)
- J. S. W. Wong, "Necessary and sufficient conditions for oscillation of second-order neutral differential equations", J. Math. Anal. Appl, 252(1), pp.342~352 (2000)
- B. G. Zhang, "Oscillation of second-order nonlinear delay dynamic equations on time scales", Comput. Math. Appl, 49(4), pp.599~609 (2005)