Journal of Analysis & Number Theory
Journal license

Journal

Journal of Analysis & Number Theory


Volume
& Issue

Volume 4, Issue 2


Published
on

July 1, 2016


Pages

105-111


DOI

Article

Oscillatory Behavior of Solutions for Forced Second Order Nonlinear Functional Integro-Dynamic Equations on Time Scales

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Authors

H. A. Agwa Affiliation:
Department of Mathematics, Faculty of Education, Ain Shams University, Roxy, Cairo, Egypt
, Ahmed M. M. Khodier Affiliation:
Department of Mathematics, Faculty of Education, Ain Shams University, Roxy, Cairo, Egypt
and Heba A. Hassan* Affiliation:
Department of Mathematics, Faculty of Education, Ain Shams University, Roxy, Cairo, Egypt


Abstract

In this paper, we deal with the oscillatory behavior of forced second order nonlinear functional integro-dynamic equations of the form $(r(t)x^\Delta (t))^\Delta = e(t) \pm p(t)x^\gamma(\tau(t)) + \int_0^t k(t,s) f(s,x(\tau(s)))\Delta s$, and $(r(t)x^\Delta (t))^\Delta = e(t) + p(t)x(\tau(t)) - \int_0^t k(t,s) f(s,x(\tau(s)))\Delta s$, on time scales $\mathbb{T}$, where $r(t)$, $p(t)$ and $e(t)$ are right dense continuous (rd-continuous) functions on $\mathbb{T}$. Oscillation behavior of these equations has not been studied before. Our results improve and extend some results established by Grace et al. [13]. We also give some examples to illustrate our main results.


Keywords

Oscillation, integro-dynamic equations, time scales


Citation

Agwa, H. A., Khodier, A. M. M., & Hassan, H. A. (2016). Oscillatory behavior of solutions for forced second order nonlinear functional integro-dynamic equations on time scales. Journal of Analysis & Number Theory, 4(2), 105–111. https://doi.org/10.18576/jant/040204

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