Oscillation of Second-Order Nonlinear Delay Dynamic Equations on Time Scales

H. A. Agwa, A. M. M. Khodier and Heba A. Hassan

International Journal of Differential Equations, 2011, vol. 2011, 1-15

Abstract:

In this work, we use the generalized Riccati transformation and the inequality technique to establish some new oscillation criteria for the second-order nonlinear delay dynamic equation ( ð ‘ ( ð ‘¡ ) ( ð ‘¥ Δ ( ð ‘¡ ) ) ð ›¾ ) Δ + ð ‘ž ( ð ‘¡ ) ð ‘“ ( ð ‘¥ ( ð œ ( ð ‘¡ ) ) ) = 0 , on a time scale ð •‹ , where ð ›¾ is the quotient of odd positive integers and p(t) and q(t) are positive right-dense continuous (rd-continuous) functions on ð •‹ . Our results improve and extend some results established by Sun et al. 2009. Also our results unify the oscillation of the second-order nonlinear delay differential equation and the second-order nonlinear delay difference equation. Finally, we give some examples to illustrate our main results.

Date: 2011
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnijde:863801

DOI: 10.1155/2011/863801

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