DOI QR코드

DOI QR Code

OSCILLATION OF SECOND ORDER NONLINEAR DELAY DIFFERENCE EQUATIONS

  • Saker, S.H. (Mathematics Department, Faculty of Science, Mansoura University)
  • Published : 2003.08.01

Abstract

In this paper we shall consider the nonlinear delay difference equation $\Delta({p_n}{\Deltax_N})\;+\;q_nf(x_{n-\sigma})\;=\;0,\;n\;=\;0,\;1,\;2,\;...$ when (equation omitted). We will establish some sufficient conditions which guarantee that every solution is oscillatory or converges to zero.

Keywords

References

  1. Theory, methods and applications(second edition) Difference Equations and Inequalities R.P.Agarwal
  2. Advanced topics in difference equations R.P.Agarwal;P.J.Y.Wong
  3. Appl. Math. Lett. v.13 Oscillation of second-order linear difference equations M.H.Abu-Risha
  4. Kyungpook Math. J. v.40 Asymptotic behavior of positive solutions of second order quasilinear difference equations R.Arul;E.Thandapani
  5. Bull. Inst. Math. Acad. Sinica v.21 A comparison theorems for asymptotically monotone solutions of nonlinear difference equations S.S.Cheng;H.J.Li
  6. Tamkang J. Math. v.21 Bounded solutions of nonlinear difference equations
  7. Funkcial. Ekvac. v.34 Oscillation criteria for second order difference equation S.S.Cheng;T.C.Yan;H.J.Li
  8. Comput. Math. Appl. v.36 Oscillation and nonlinear difference equations S.C.Fu;L.Y.Tsai https://doi.org/10.1016/S0898-1221(98)80020-5
  9. J. Math. Anal. Appl. v.216 Oscillation and nonoscillation theorems for certain second-order difference equations with forcing term S.R.Grace;H.A.El-Morshedy https://doi.org/10.1006/jmaa.1997.5692
  10. J. Math. Anal. Appl. v.175 Oscillatory and asymptotic behavior of second order nonlinear difference equations X.Z.He https://doi.org/10.1006/jmaa.1993.1186
  11. Utilitas Mathematica v.44 An oscillation theorem for a second order nonlinear difference equation H.J.Li;S.S.Cheng
  12. Tamkang J. Math. v.24 Asymptotically monotone solutions of a nonlinear difference equation
  13. Math. Comput. Modelling v.31 Oscillation theorems for second order nonlinear difference equations W.T.Li https://doi.org/10.1016/S0895-7177(00)00047-9
  14. Comp. Math. Appl. v.36 Oscillation cruteria for a nonlinear difference equations W.T.Li;S.S.Cheng
  15. J. Math. Anal.Appl. v.246 On unbounded positive solutions of second order difference equations with a singular nonlinear term W.T.Li;X.L.Fan;C.K.Zhong https://doi.org/10.1006/jmaa.2000.6753
  16. Kyungpook Math. J. v.39 Oscillation criteria for second order nonlinear delay difference equations Z.R.Liu;W.D.Chen;Y.H.Yu
  17. Arch. Math. v.53 Oscillation theorems for linear differential equations of second order Ch.G.Philos https://doi.org/10.1007/BF01324723
  18. J. Math. Anal. Appl. v.252 Hartman-Wintner type lemma, oscillation and conjugacy criteria for half-linear difference equations P.Rehak https://doi.org/10.1006/jmaa.2000.7124
  19. Electron. J. Differential Equations 2002 v.2002 no.68 Kamenev-type oscillation criteria for forced Emden-Fowler superlinear difference equations S.H.Saker
  20. Applied Math. Comput. v.142 New oscilation criteria for second-order nonlinear neutral delay difference equations https://doi.org/10.1016/S0096-3003(02)00286-2
  21. Appl. Math. Comput. Ocillation second-order perturbed nonlinear difference equations
  22. Bull. Polish. Acad. Sci. Math. v.34 Characterization of oscillation of second order nonlinear difference equations B. Szmanda
  23. Appl. Math. Lett. v.13 Oscillation of second-order half-linear difference equations E.Thandapani;K.Ravi
  24. J. Math. Anal. Appl. v.173 Oscillation and asymptotic behaivior of second order difference equations B.G.Zhang https://doi.org/10.1006/jmaa.1993.1052
  25. Comput. Math. Appl. v.38 Oscillation criteria for second-order functional difference equations with summation small coefficients Z.Zhang;J.Zhang https://doi.org/10.1016/S0898-1221(99)00165-0

Cited by

  1. Monotonicity of Eventually Positive Solutions for a Second Order Nonlinear Difference Equation vol.2013, 2013, https://doi.org/10.1155/2013/635149
  2. Oscillation of Second Order Nonlinear Delay Damped Difference Equations vol.23, pp.4, 2007, https://doi.org/10.1007/s10114-005-0792-1
  3. Oscillation Criteria of Solution for a Second Order Difference Equation with Forced Term vol.2010, 2010, https://doi.org/10.1155/2010/171234
  4. Oscillation for second-order nonlinear neutral delay difference equations vol.163, pp.2, 2005, https://doi.org/10.1016/j.amc.2004.04.017