Article
Oscillatory Behavior of Solutions for Forced Second Order Nonlinear Functional Integro-Dynamic Equations on Time Scales
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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
H. A. Agwa, A. M. M. Khodier and H. A. Hassan, “Oscillatory behavior of solutions for forced second order nonlinear functional integro-dynamic equations on time scales,” Journal of Analysis & Number Theory, vol. 4, no. 2, pp. 105–111, 2016, doi: 10.18576/jant/040204.
Agwa HA, Khodier AMM, Hassan HA. Oscillatory behavior of solutions for forced second order nonlinear functional integro-dynamic equations on time scales. Journal of Analysis & Number Theory. 2016;4(2):105–111. doi:10.18576/jant/040204.
Agwa, H. A., Khodier, A. M. M. and 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), pp. 105–111. Available at: https://doi.org/10.18576/jant/040204.
Agwa, H. A., et al. “Oscillatory Behavior of Solutions for Forced Second Order Nonlinear Functional Integro-dynamic Equations on Time Scales.” Journal of Analysis & Number Theory, vol. 4, no. 2, 2016, pp. 105–111. https://doi.org/10.18576/jant/040204.
Agwa, H. A., Ahmed M. M. Khodier, and Heba A. Hassan. “Oscillatory Behavior of Solutions for Forced Second Order Nonlinear Functional Integro-dynamic Equations on Time Scales.” Journal of Analysis & Number Theory 4, no. 2 (2016): 105–111. https://doi.org/10.18576/jant/040204.
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Published by: Engineering Journals


