Title: Oscillation Criteria for Second-Order Nonlinear Functional Dynamic Equations with Damping on Time Scales
Author(s): Emine Tuğla, Fatma Serap Topal
Pages: 42-51
Cite as:
Emine Tuğla, Fatma Serap Topal, Oscillation Criteria for Second-Order Nonlinear Functional Dynamic Equations with Damping on Time Scales, Int. J. Anal. Appl., 14 (1) (2017), 42-51.

Abstract


In this paper, we study oscillatory behavior of second-order dynamic equations with damping under some assumptions on time scales. New theorems extend and improve the results in the literature. Illustrative examples are given.

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References


  1. S. Hilger, Analysis on measure chains-A unified approach to continuous and discrete calculus, Results Math. 18 (1990) 18-56.

  2. M. Bohner, A. Peterson, Dynamic Equations on time scales, An Introduction with Applications, Birkhäuser, Boston, 2001.

  3. M. Bohner and A. Peterson (Eds), Advances in Dynamic Equations on Time Scales, Birkhäuser, Boston, 2003.

  4. R.P. Agarwal, M. Bohner, D. O’Regan, A. Peterson, Dynamic equations on time scales: a survey, J. Comput. And Appl. Math. 141 (1-2)(2002) 1-26.

  5. R.P. Agarwal, M. Bohner, S.H. Saker, Oscillation of second order delay dynamic equations, Can. Appl. Math. Q. 13 (2005) 1-18.

  6. H.A. Agwa, A.M.M. Khodier, H.A. Hassan, Oscillation of second-order nonlinear delay dynamic equations on time scales, Int. J. Differ. Equ. 2011 (2011) Article ID 863801.

  7. M. Bohner, Some oscillation criteria for first order delay dynamic equations, Far East J. Appl. Math. 18 (3)(2005) 289-304.

  8. M. Bohner, S. H. Saker, Oscillation of second order nonlinear dynamic equations on time scales, Rocky Mountain J. Math. 34 (4) (2004) 1239-1254.

  9. D.X. Chen, P.X. Qu, Y.H. Lan, Oscillation of second-order nonlinear dynamic equations with positive and negative coefficients, Adv. Differ. Equ. 2013 (2013) Art. ID 168.

  10. L. Erbe, A. Peterson, S.H. Saker, Oscillation criteria for second-order nonlinear dynamic equations on time scales, J. Lond. Math. Soc. 67 (3) (2003) 701-714.

  11. L. Erbe, A. Peterson, S.H. Saker, Oscillation criteria for second-order nonlinear delay dynamic equations, J. Math. Anal. Appl. 333 (1) (2007) 505-522.

  12. L. Erbe, T. Hassan, A. Peterson, Oscillation of second order functional dynamic equations, Int. J. Differ. Equ. 5 (2) (2010) 175-193.

  13. T.S. Hassan, Oscillation criteria for half-linear dynamic equations on time scales, J. Math. Anal. Appl. 345 (1) (2008) 176-185.

  14. S.H. Saker, Oscillation criteria of second-order half-linear dynamic equations on time scales, J. Comput. Appl. Math. 177 (2) (2005) 375-387.

  15. S. Sun, Z. Han, C. Zhang, Oscillation of second-order delay dynamic equations on time scales, J. Appl. Math. Comput. 30 (1-2) (2009) 459-468.

  16. Y. S . ahiner, Oscillation of second-order delay differential equations on time scales, Nonlinear Anal., Theory, Methods Appl. 63 (5-7) (2005) 1073-1080.

  17. M.T. S . enel, Oscillation theorems for the second order damped nonlinear dynamic equation on time scales, Contemp. Anal. Appl. Math. 1 (2) (2013) 167-180.

  18. Q. Zhang, Oscillation of second-order half-linear delay dynamic equations with damping on time scales, J. Comput. Appl. Math. 235 (5) (2011) 1180-1188.

  19. Q. Zhang, L. Gao, Oscillation of second-order nonlinear delay dynamic equations with damping on time scales, J. Appl. Math. Comput. 37 (1-2) (2011) 145-158.

  20. Q. Zhang, L. Gao, L. Wang, Oscillation of second-order nonlinear delay dynamic equations on time scales, Comput. Math. Appl. 61 (8) (2011) 2342-2348.