1Department of Mathematics, Faculty of Education, Ain Shams University, Roxy, Cairo, 2Department of Mathematics, Faculty of Education, Ain Shams University, Roxy, Cairo
Acta mathematica Universitatis Comenianae, Tome 84 (2015) no. 1, pp. 133-148
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Heba M. Atteya; H. A. Agwa; A. M. M. Khodier; Heba M. Atteya; H. A. Agwa; A. M. M. Khodier. Oscillation of second-order nonlinear forced dynamic equations with damping on time scales. Acta mathematica Universitatis Comenianae, Tome 84 (2015) no. 1, pp. 133-148. http://geodesic.mathdoc.fr/item/AMUC_2015_84_1_a11/
@article{AMUC_2015_84_1_a11,
author = {Heba M. Atteya and H. A. Agwa and A. M. M. Khodier and Heba M. Atteya and H. A. Agwa and A. M. M. Khodier},
title = { Oscillation of second-order nonlinear forced dynamic equations with damping on time scales},
journal = {Acta mathematica Universitatis Comenianae},
pages = {133--148},
year = {2015},
volume = {84},
number = {1},
url = {http://geodesic.mathdoc.fr/item/AMUC_2015_84_1_a11/}
}
TY - JOUR
AU - Heba M. Atteya
AU - H. A. Agwa
AU - A. M. M. Khodier
AU - Heba M. Atteya
AU - H. A. Agwa
AU - A. M. M. Khodier
TI - Oscillation of second-order nonlinear forced dynamic equations with damping on time scales
JO - Acta mathematica Universitatis Comenianae
PY - 2015
SP - 133
EP - 148
VL - 84
IS - 1
UR - http://geodesic.mathdoc.fr/item/AMUC_2015_84_1_a11/
ID - AMUC_2015_84_1_a11
ER -
%0 Journal Article
%A Heba M. Atteya
%A H. A. Agwa
%A A. M. M. Khodier
%A Heba M. Atteya
%A H. A. Agwa
%A A. M. M. Khodier
%T Oscillation of second-order nonlinear forced dynamic equations with damping on time scales
%J Acta mathematica Universitatis Comenianae
%D 2015
%P 133-148
%V 84
%N 1
%U http://geodesic.mathdoc.fr/item/AMUC_2015_84_1_a11/
%F AMUC_2015_84_1_a11
In this paper, we use Riccati transformation technique to establish some new oscillation criteria for the second-order nonlinear forced dynamic equation with damping on a time scale T$$(r(t)g(x^{\Delta}(t)))^{\Delta} + p(t)g(x(t)) + q(t)f(x^{\sigma}(t)) = G(t; x^{\sigma}(t));$$where $r(t), p(t)$ and $q(t)$ are real-valued right continuous functions on T and no sign conditions are imposed on these functions. The function $f : T \to T$ is continuouslydifferentiable and nondecreasing such that $xf(x) > 0$ for $x \neq 0$. Our results not only generalize and extend some existing results, but also can be applied to the oscillationproblems that are not covered in literature. Finally, we give some examples to illustrateour main results.
