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

2016 ◽  
Vol 4 (2) ◽  
pp. 105-111
Author(s):  
H. A. Agwa ◽  
Ahmed M. M. Khodier ◽  
Heba A. Hassan
Keyword(s):  
Time Scales ◽  
Oscillatory Behavior ◽  
Second Order ◽  
Dynamic Equations ◽  
Nonlinear Functional

scholarly journals Oscillatory and asymptotic behavior of solutions for second-order mixed nonlinear integro-dynamic equations with maxima on time scales

Filomat ◽  
2019 ◽  
Vol 33 (10) ◽  
pp. 2907-2929
Author(s):  
Hassan Agwa ◽  
Mokhtar Naby ◽  
Heba Arafa
Keyword(s):  
Asymptotic Behavior ◽  
Time Scales ◽  
Oscillatory Behavior ◽  
Second Order ◽  
Dynamic Equations ◽  
Asymptotic Behavior Of Solutions

This paper is concerned with the oscillatory and asymptotic behavior for solutions of the following second-order mixed nonlinear integro-dynamic equations with maxima on time scales (r(t)(z?(t))?)? + ?t0 a(t,s) f(s, x(s))?s + ?n,i=1 qi(t) max s?[?i(t),?i(t)] x?(s) = 0, where z(t) = x(t) + p1(t)x(?1(t)) + p2(t)x(?2(t)), t ? [0,+?)T. The oscillatory behavior of this equation hasn?t been discussed before, also our results improve and extend some results established by Grace et al. [2] and [8].

scholarly journals New Oscillatory Behavior of Second-Order Nonlinear Dynamic Equations with Damping on Time Scales

2014 ◽  
Vol 2014 ◽  
pp. 1-5
Author(s):  
Shouhua Liu ◽  
Quanxin Zhang
Keyword(s):  
Time Scales ◽  
Nonlinear Dynamic ◽  
Oscillatory Behavior ◽  
Second Order ◽  
Dynamic Equations ◽  
Oscillation Criteria ◽  
Nonlinear Dynamic Equations

We establish four new oscillation criteria of Grace-type for the second-order nonlinear dynamic equations with damping. These criteria extend known criteria for corresponding dynamic equations. Our results are new even in the continuous and the discrete cases.

scholarly journals Oscillation Theorems for Second-Order Half-Linear Advanced Dynamic Equations on Time Scales

2011 ◽  
Vol 2011 ◽  
pp. 1-16 ◽  
Author(s):  
Shuhong Tang ◽  
Tongxing Li ◽  
Ethiraju Thandapani
Keyword(s):  
Differential Equation ◽  
Difference Equation ◽  
Time Scales ◽  
Dynamic Equation ◽  
Time Scale ◽  
Sufficient Conditions ◽  
Oscillatory Behavior ◽  
Second Order ◽  
Dynamic Equations ◽  
Oscillation Theorems

This paper is concerned with the oscillatory behavior of the second-order half-linear advanced dynamic equation on an arbitrary time scale with sup , where and . Some sufficient conditions for oscillation of the studied equation are established. Our results not only improve and complement those results in the literature but also unify the oscillation of the second-order half-linear advanced differential equation and the second-order half-linear advanced difference equation. Three examples are included to illustrate the main results.

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