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Oscillatory Behavior of Solutions for Forced Second Order Nonlinear Functional Integro-Dynamic Equations on Time Scales |
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PP: 105-111 |
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doi:10.18576/jant/040204
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Author(s) |
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H. A. Agwa,
Ahmed M. M. Khodier,
Heba A. Hassan,
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Abstract |
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| In this paper, we deal with the oscillatory behavior of forced second order nonlinear functional integro-dynamic equations
of the form
(r(t)xD (t))D = e(t)± p(t)xg (t (t))+Z t
0
k(t, s) f (s, x(t (s)))D s,
and
(r(t)xD (t))D = e(t)+ p(t)x(t (t))−Z t
0
k(t, s) f (s, x(t (s)))D s,
on time scales T, where r(t), p(t) and e(t) are right dense continuous (rd-continuous) functions on T. Oscillation behavior of these
equations dose not 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. |
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