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Oscillation of third order functional dynamic equations with mixed arguments on time scales

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Abstract

In this paper we investigate the oscillation of third order nonlinear functional dynamic equation with mixed arguments. Our results extend and improve many known results for oscillation of third order dynamic equations. Some examples are given to illustrate the main results.

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References

  1. Bohner, M., Peterson, A.: Dynamic Equations on Time Scales: An Introduction with Applications. Birkhäuser, Boston (2001)

    MATH  Google Scholar 

  2. Bohner, M., Peterson, A. (eds.): Advances in Dynamic Equations on Time Scales. Birkhäuser, Boston (2003)

    MATH  Google Scholar 

  3. Došlý, O., Hilger, E.: A necessary and sufficient condition for oscillation of the Sturm-Liouville dynamic equation on time scales. J. Comput. Appl. Math. 141(1–2), 571–585 (2002). Special Issue on Dynamic Equations on Time Scales (P.P. Agarwal, M. Bohner and D. O’Regan, eds.)

    Google Scholar 

  4. Elabbasy, E.M., Hassan, T.S.: Oscillation of third order nonlinear functional differential equations. Differ. Equ. Appl. (submitted)

  5. Erbe, L., Hassan, T.S., Peterson, A.: Oscillation criteria for nonlinear damped dynamic equations on time scales. Appl. Math. Comput. 203, 343–357 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  6. Erbe, L., Hassan, T.S., Peterson, A.: Oscillation criteria for nonlinear functional neutral dynamic equations on time scales. J. Differ. Equ. Appl. (to appear)

  7. Erbe, L., Hassan, T.S., Peterson, A., Saker, S.H.: Oscillation criteria for half-linear delay dynamic equations on time scales. Nonlinear Dyn. Syst. Theory 9, 51–68 (2009)

    MATH  MathSciNet  Google Scholar 

  8. Erbe, L., Hassan, T.S., Peterson, A., Saker, S.H.: Oscillation criteria for sublinear half-linear delay dynamic equations on time scales. Int. J. Differ. Equ. 3, 227–245 (2008)

    MathSciNet  Google Scholar 

  9. Erbe, L., Peterson, A., Saker, S.H.: Asymptotic behavior of solutions of a third-order nonlinear dynamic equation on time scales. J. Comput. Appl. Math. 181, 92–102 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  10. Erbe, L., Peterson, A., Saker, S.H.: Hille and Nehari type criteria for third order dynamic equations. J. Math. Anal. Appl. 329, 112–131 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  11. Erbe, L., Peterson, A., Saker, S.H.: Oscillation and asymptotic behavior of a third-order nonlinear dynamic equation. Can. Q. Appl. Math. 14, 2 (2006)

    MathSciNet  Google Scholar 

  12. Erbe, L., Hassan, T.S., Peterson, A.: Oscillation of third order nonlinear functional dynamic equations on time scales. Differ. Equ. Dyn. Syst. (2009, in press)

  13. Hardy, G.H., Littlewood, J.E., Polya, G.: Inequalities, 2nd edn. Cambridge University Press, Cambridge (1988)

    MATH  Google Scholar 

  14. Hassan, T.S.: Oscillation of third order nonlinear delay dynamic equations on time scales. Math. Comput. Model. 49, 1573–1586 (2009)

    Article  MATH  MathSciNet  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  16. Hilger, S.: Analysis on measure chains—a unified approach to continuous and discrete calculus. Results Math. 18, 18–56 (1990)

    MATH  MathSciNet  Google Scholar 

  17. Kac, V., Chueng, P.: Quantum Calculus. Universitext (2002)

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Author notes

  1. Taher S. Hassan

    Present address: Department of Mathematics, University of Nebraska–Lincoln, Lincoln, NE, 68588-0130, USA

Authors and Affiliations

  1. Department of Mathematics, University of Nebraska–Lincoln, Lincoln, NE, 68588-0130, USA

    Lynn Erbe & Allan Peterson

  2. Department of Mathematics, Faculty of Science, Mansoura University, Mansoura, 35516, Egypt

    Taher S. Hassan

Authors
  1. Lynn Erbe
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  2. Taher S. Hassan
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  3. Allan Peterson
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Correspondence to Taher S. Hassan.

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Erbe, L., Hassan, T.S. & Peterson, A. Oscillation of third order functional dynamic equations with mixed arguments on time scales. J. Appl. Math. Comput. 34, 353–371 (2010). https://doi.org/10.1007/s12190-009-0326-6

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  • DOI: https://doi.org/10.1007/s12190-009-0326-6

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