OSCILLATION STUDIES ON SECOND ORDER DAMPED NONLINEAR DELAY DYNAMIC EQUATIONS ON TIME SCALES

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Published: 2016-06-10

Page: 188-200


H. A. AGWA

Department of Mathematics, Faculty of Education, Ain Shams University, P.O.Box 11757, Cairo, Egypt.

AHMED M. M. KHODIER

Department of Mathematics, Faculty of Education, Ain Shams University, P.O.Box 11757, Cairo, Egypt.

HEBA A. HASSAN *

Department of Mathematics, Faculty of Education, Ain Shams University, P.O.Box 11757, Cairo, Egypt.

*Author to whom correspondence should be addressed.


Abstract

This paper concerns the oscillation of solutions to the second order nonlinear delay dynamic equation with damping on a time scale 


                          (r(t)ψ(xΔ(t)))Δ + p(t)ψ(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 . Our results complement the results in Şenel [1]. Our results in the special cases when the time scale is the set of real numbers or integers involve and improve some oscillation results for the second-order differential and difference equations respectively. Finally, we give some examples to illustrate our main results.

Keywords: Time scales, oscillation criteria, second order delay dynamic equations, generalized Riccati technique, generalized exponential function


How to Cite

AGWA, H. A., KHODIER, A. M. M., & HASSAN, H. A. (2016). OSCILLATION STUDIES ON SECOND ORDER DAMPED NONLINEAR DELAY DYNAMIC EQUATIONS ON TIME SCALES. Asian Journal of Mathematics and Computer Research, 12(3), 188–200. Retrieved from https://ikprress.org/index.php/AJOMCOR/article/view/621

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