Necessary and sufficient conditions on the asymptotic behavior of second-order neutral delay dynamic equations with positive and negative coefficients

2013 ◽  
Vol 37 (8) ◽  
pp. 1219-1231 ◽  
Author(s):  
B. Karpuz
Keyword(s):  
Asymptotic Behavior ◽  
Sufficient Conditions ◽  
Second Order ◽  
Necessary And Sufficient Conditions ◽  
Dynamic Equations ◽  
Neutral Delay ◽  
Positive And Negative Coefficients ◽  
Delay Dynamic Equations ◽  
Necessary And Sufficient

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.

On oscillatory and asymptotic behavior of fourth order nonlinear neutral delay dynamic equations with positive and negative coefficients

2014 ◽  
Vol 64 (2) ◽  
Author(s):  
John Graef ◽  
Saroj Panigrahi ◽  
P. Reddy
Keyword(s):  
Fixed Point ◽  
Fourth Order ◽  
Asymptotic Properties ◽  
Sufficient Conditions ◽  
Dynamic Equations ◽  
Neutral Delay ◽  
Positive And Negative Coefficients ◽  
Delay Dynamic Equations ◽  
Krasnosel’Skii’S Fixed Point Theorem ◽  
Neutral Dynamic Equations

AbstractIn this paper, oscillatory and asymptotic properties of solutions of nonlinear fourth order neutral dynamic equations of the form $(r(t)(y(t) + p(t)y(\alpha _1 (t)))^{\Delta ^2 } )^{\Delta ^2 } + q(t)G(y(\alpha _2 (t))) - h(t)H(y(\alpha _3 (t))) = 0(H)$ and $(r(t)(y(t) + p(t)y(\alpha _1 (t)))^{\Delta ^2 } )^{\Delta ^2 } + q(t)G(y(\alpha _2 (t))) - h(t)H(y(\alpha _3 (t))) = f(t),(NH)$ are studied on a time scale $\mathbb{T}$ under the assumption that $\int\limits_{t_0 }^\infty {\tfrac{t} {{r(t)}}\Delta t = \infty } $ and for various ranges of p(t). In addition, sufficient conditions are obtained for the existence of bounded positive solutions of the equation (NH) by using Krasnosel’skii’s fixed point theorem.

scholarly journals Necessary and Sufficient Conditions for Oscillatory and Asymptotic Behaviour of Solutions to Second-Order Nonlinear Neutral Differential Equations with Several Delays

2020 ◽  
Vol 75 (1) ◽  
pp. 121-134 ◽  
Author(s):  
Shyam Sundar Santra
Keyword(s):  
Differential Equations ◽  
Sufficient Conditions ◽  
Main Tool ◽  
Second Order ◽  
Necessary And Sufficient Conditions ◽  
Asymptotic Behavior Of Solutions ◽  
Neutral Delay ◽  
Neutral Differential Equations ◽  
Several Delays ◽  
Necessary And Sufficient

AbstractIn this paper, necessary and sufficient conditions are obtained for oscillatory and asymptotic behavior of solutions to second-order nonlinear neutral delay differential equations of the form {d \over {dt}}\left[ {r\left( t \right){{\left[ {{d \over {dt}}\left( {x\left( t \right) + p\left( t \right)x\left( {t - \tau } \right)} \right)} \right]}^\alpha }} \right] + \sum\limits_{i = 1}^m {{q_i}\left( t \right)H\left( {x\left( {t - {\sigma _i}} \right)} \right) = 0\,\,\,{\rm{for}}\,t \ge {t_0} > 0,}under the assumption ∫∞(r(n))−1/αdη=∞. Our main tool is Lebesque’s dominated convergence theorem. Further, some illustrative examples showing the applicability of the new results are included.

scholarly journals Second-order impulsive differential systems with mixed and several delays

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Shyam Sundar Santra ◽  
Apurba Ghosh ◽  
Omar Bazighifan ◽  
Khaled Mohamed Khedher ◽  
Taher A. Nofal
Keyword(s):  
Differential Equations ◽  
Sufficient Conditions ◽  
Impulsive Differential Equations ◽  
Oscillation Theory ◽  
Second Order ◽  
Neutral Delay ◽  
Differential Systems ◽  
Impulsive Differential Systems ◽  
Several Delays ◽  
Necessary And Sufficient

AbstractIn this work, we present new necessary and sufficient conditions for the oscillation of a class of second-order neutral delay impulsive differential equations. Our oscillation results complement, simplify and improve recent results on oscillation theory of this type of nonlinear neutral impulsive differential equations that appear in the literature. An example is provided to illustrate the value of the main results.

Asymptotic behavior of the records of multivariate random sequences in a norm sense

2020 ◽  
Vol 70 (6) ◽  
pp. 1457-1468
Author(s):  
Haroon M. Barakat ◽  
M. H. Harpy
Keyword(s):  
Asymptotic Behavior ◽  
Weak Convergence ◽  
Sufficient Conditions ◽  
Record Values ◽  
Necessary And Sufficient Conditions ◽  
Random Sequences ◽  
Necessary And Sufficient

AbstractIn this paper, we investigate the asymptotic behavior of the multivariate record values by using the Reduced Ordering Principle (R-ordering). Necessary and sufficient conditions for weak convergence of the multivariate record values based on sup-norm are determined. Some illustrative examples are given.

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