Oscillation of Second-Order Nonlinear Delay Dynamic Equations with Damping on Time Scales
We use the generalized Riccati transformation and the inequality technique to establish some new oscillation criteria for the second-order nonlinear delay dynamic equation with damping on a time scale T(r(t)g(x(t), xΔ(t)))Δ+p(t)g(x(t), xΔ(t)) + q(t)f(x(τ(t)))=0, where r(t), p(t), and q(t) are posit...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | International Journal of Differential Equations |
| Online Access: | http://dx.doi.org/10.1155/2014/594376 |
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| author | H. A. Agwa Ahmed M. M. Khodier Heba A. Hassan |
| author_facet | H. A. Agwa Ahmed M. M. Khodier Heba A. Hassan |
| author_sort | H. A. Agwa |
| collection | DOAJ |
| description | We use the generalized Riccati transformation and the inequality technique to establish some new oscillation criteria for the second-order nonlinear delay dynamic equation with damping on a time scale T(r(t)g(x(t), xΔ(t)))Δ+p(t)g(x(t), xΔ(t)) + q(t)f(x(τ(t)))=0, where r(t), p(t), and q(t) are positive right dense continuous (rd-continuous) functions on T. Our results improve and extend some results established by Zhang et al., 2011. Also, our results unify the oscillation of the second-order nonlinear delay differential equation with damping and the second-order nonlinear delay difference equation with damping. Finally, we give some examples to illustrate our main results. |
| format | Article |
| id | doaj-art-fa6a58b8eff64dbf94f0fe32011151c1 |
| institution | Kabale University |
| issn | 1687-9643 1687-9651 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Differential Equations |
| spelling | doaj-art-fa6a58b8eff64dbf94f0fe32011151c12025-02-03T05:44:53ZengWileyInternational Journal of Differential Equations1687-96431687-96512014-01-01201410.1155/2014/594376594376Oscillation of Second-Order Nonlinear Delay Dynamic Equations with Damping on Time ScalesH. A. Agwa0Ahmed M. M. Khodier1Heba A. Hassan2Department of Mathematics, Faculty of Education, Ain Shams University, Roxy, Cairo 11757, EgyptDepartment of Mathematics, Faculty of Education, Ain Shams University, Roxy, Cairo 11757, EgyptDepartment of Mathematics, Faculty of Education, Ain Shams University, Roxy, Cairo 11757, EgyptWe use the generalized Riccati transformation and the inequality technique to establish some new oscillation criteria for the second-order nonlinear delay dynamic equation with damping on a time scale T(r(t)g(x(t), xΔ(t)))Δ+p(t)g(x(t), xΔ(t)) + q(t)f(x(τ(t)))=0, where r(t), p(t), and q(t) are positive right dense continuous (rd-continuous) functions on T. Our results improve and extend some results established by Zhang et al., 2011. Also, our results unify the oscillation of the second-order nonlinear delay differential equation with damping and the second-order nonlinear delay difference equation with damping. Finally, we give some examples to illustrate our main results.http://dx.doi.org/10.1155/2014/594376 |
| spellingShingle | H. A. Agwa Ahmed M. M. Khodier Heba A. Hassan Oscillation of Second-Order Nonlinear Delay Dynamic Equations with Damping on Time Scales International Journal of Differential Equations |
| title | Oscillation of Second-Order Nonlinear Delay Dynamic Equations with Damping on Time Scales |
| title_full | Oscillation of Second-Order Nonlinear Delay Dynamic Equations with Damping on Time Scales |
| title_fullStr | Oscillation of Second-Order Nonlinear Delay Dynamic Equations with Damping on Time Scales |
| title_full_unstemmed | Oscillation of Second-Order Nonlinear Delay Dynamic Equations with Damping on Time Scales |
| title_short | Oscillation of Second-Order Nonlinear Delay Dynamic Equations with Damping on Time Scales |
| title_sort | oscillation of second order nonlinear delay dynamic equations with damping on time scales |
| url | http://dx.doi.org/10.1155/2014/594376 |
| work_keys_str_mv | AT haagwa oscillationofsecondordernonlineardelaydynamicequationswithdampingontimescales AT ahmedmmkhodier oscillationofsecondordernonlineardelaydynamicequationswithdampingontimescales AT hebaahassan oscillationofsecondordernonlineardelaydynamicequationswithdampingontimescales |