scholarly journals Asymptotic Behavior of Solutions of Higher-Order Dynamic Equations on Time Scales

2011 ◽  
Vol 2011 ◽  
pp. 1-14 ◽  
Author(s):  
Taixiang Sun ◽  
Hongjian Xi ◽  
Xiaofeng Peng
Keyword(s):  
Asymptotic Behavior ◽  
Time Scales ◽  
Higher Order ◽  
Dynamic Equations ◽  
Asymptotic Behavior Of Solutions

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 Oscillation Criteria for Third-Order Nonlinear Neutral Dynamic Equations with Mixed Deviating Arguments on Time Scales

Mathematics ◽  
2021 ◽  
Vol 9 (5) ◽  
pp. 552
Author(s):  
Zhiyu Zhang ◽  
Ruihua Feng ◽  
Irena Jadlovská ◽  
Qingmin Liu
Keyword(s):  
Asymptotic Behavior ◽  
Time Scales ◽  
Dynamic Equations ◽  
Asymptotic Behavior Of Solutions ◽  
Riccati Transformation ◽  
Third Order ◽  
Deviating Arguments ◽  
Oscillation Criteria ◽  
Inequality Technique ◽  
Neutral Dynamic Equations

Under a couple of canonical and mixed canonical-noncanonical conditions, we investigate the oscillation and asymptotic behavior of solutions to a class of third-order nonlinear neutral dynamic equations with mixed deviating arguments on time scales. By means of the double Riccati transformation and the inequality technique, new oscillation criteria are established, which improve and generalize related results in the literature. Several examples are given to illustrate the main results.

Oscillatory behavior of higher order nonlinear homogeneous neutral delay dynamic equations with positive and negative coefficients

2018 ◽  
Vol 24 (2) ◽  
pp. 139-154
Author(s):  
Saroj Panigrahi ◽  
P. Rami Reddy
Keyword(s):  
Asymptotic Behavior ◽  
Fourth Order ◽  
Sufficient Conditions ◽  
Higher Order ◽  
Oscillatory Behavior ◽  
Dynamic Equations ◽  
Asymptotic Behavior Of Solutions ◽  
Neutral Delay ◽  
Positive And Negative Coefficients ◽  
Delay Dynamic Equations

Abstract In this paper, we derive some sufficient conditions for the oscillatory and asymptotic behavior of solutions of the higher order nonlinear neutral delay dynamic equation with positive and negative coefficients. The results of this paper extend and generalize the results of [S. Panigrahi and P. Rami Reddy, Oscillatory and asymptotic behavior of fourth order non-linear neutral delay dynamic equations, Dyn. Contin. Discrete Impuls. Syst. Ser. A Math. Anal. 20 2013, 143–163] and [S. Panigrahi, J. R. Graef and P. Rami Reddy, Oscillation results for fourth order nonlinear neutral dynamic equations, Commun. Math. Anal. 15 2013, 11–28]. Examples are included to illustrate the validation of the results.

Asymptotic behavior of solutions of forced third-order dynamic equations

Analysis ◽  
2019 ◽  
Vol 39 (1) ◽  
pp. 1-6 ◽  
Author(s):  
Martin Bohner ◽  
Said R. Grace ◽  
Irena Jadlovská
Keyword(s):  
Asymptotic Behavior ◽  
Time Scales ◽  
Dynamic Equations ◽  
Asymptotic Behavior Of Solutions ◽  
Nonlinear Functions ◽  
Third Order ◽  
Nonoscillatory Solutions ◽  
All Solutions

Abstract This paper deals with asymptotic behavior of nonoscillatory solutions of certain third-order forced dynamic equations on time scales. The main goal is to investigate when all solutions behave at infinity like certain nontrivial nonlinear functions.

scholarly journals Some Oscillation Criteria for Higher-Order Neutral Emden-Fowler Delay Dynamic Equations on Time Scales

2018 ◽  
Vol 228 ◽  
pp. 01003
Author(s):  
Ying Sui ◽  
Yulong Shi ◽  
Yibin Sun ◽  
Shurong Sun
Keyword(s):  
Time Scales ◽  
Dynamic Equation ◽  
Higher Order ◽  
Delay Equation ◽  
Dynamic Equations ◽  
Neutral Delay ◽  
Oscillation Criteria ◽  
Delay Dynamic Equations

New oscillation criteria are established for higher-order Emdn-Fowler dynamic equation $ q(v)x^{\beta } (\delta (v)) + (r(v)(z^{{\Delta ^{{n - 1}} }} (v))^{\alpha } )^{\Delta } = 0 $ on time scales, $ z(v): = p(v)x(\tau (v)) + x(v) $ Our results extend and supplement those reported in literatures in the sense that we study a more generalized neutral delay equation and do not require $ r^{\Delta } (v) \ge 0 $ and the commutativity of the jump and delay operators.

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