scholarly journals Oscillation for nonlinear second order dynamic equations on a time scale

2005 ◽  
Vol 301 (2) ◽  
pp. 491-507 ◽  
Author(s):  
Martin Bohner ◽  
Lynn Erbe ◽  
Allan Peterson
Keyword(s):  
Time Scale ◽  
Second Order ◽  
Dynamic Equations

scholarly journals Oscillation Criteria for Second Order Impulsive Delay Dynamic Equations on Time Scale

2021 ◽  
Vol 45 (4) ◽  
pp. 531-542
Author(s):  
GOKULA NANDA CHHATRIA ◽  
Keyword(s):  
Time Scale ◽  
Second Order ◽  
Dynamic Equations ◽  
Riccati Transformation ◽  
Transformation Technique ◽  
Oscillation Criteria ◽  
Delay Dynamic Equations ◽  
Impulsive Delay

In this work, we study the oscillation of a kind of second order impulsive delay dynamic equations on time scale by using impulsive inequality and Riccati transformation technique. Some examples are given to illustrate our main results.

scholarly journals Improved Oscillation Results for Functional Nonlinear Dynamic Equations of Second Order

Mathematics ◽  
2020 ◽  
Vol 8 (11) ◽  
pp. 1897
Author(s):  
Taher S. Hassan ◽  
Yuangong Sun ◽  
Amir Abdel Menaem
Keyword(s):  
Dynamic Equation ◽  
Time Scale ◽  
Nonlinear Dynamic ◽  
Recent Literature ◽  
Second Order ◽  
Dynamic Equations ◽  
Oscillation Criteria ◽  
Arbitrary Time ◽  
Nonlinear Dynamic Equations ◽  
Type Oscillation

In this paper, the functional dynamic equation of second order is studied on an arbitrary time scale under milder restrictions without the assumed conditions in the recent literature. The Nehari, Hille, and Ohriska type oscillation criteria of the equation are investigated. The presented results confirm that the study of the equation in this formula is superior to other previous studies. Some examples are addressed to demonstrate the finding.

scholarly journals On the Oscillation of Second Order Nonlinear Neutral Delay Dynamic Equations

2007 ◽  
Vol 14 (4) ◽  
pp. 597-606
Author(s):  
Hassan A. Agwo
Keyword(s):  
Dynamic Equation ◽  
Time Scale ◽  
Second Order ◽  
Dynamic Equations ◽  
Sufficient Condition ◽  
Neutral Delay ◽  
Oscillation Criteria ◽  
Delay Dynamic Equation ◽  
Neutral Delay Dynamic Equation ◽  
Delay Dynamic Equations

Abstract In this paper we obtain some new oscillation criteria for the second order nonlinear neutral delay dynamic equation (𝑥(𝑡) – 𝑝(𝑡)𝑥(𝑡 – τ 1))ΔΔ + 𝑞(𝑡)𝑓(𝑥(𝑡 – τ 2)) = 0, on a time scale 𝕋. Moreover, a new sufficient condition for the oscillation sublinear equation (𝑥(𝑡) – 𝑝(𝑡)𝑥(𝑡 – τ 1))″ + 𝑞(𝑡)𝑓(𝑥(𝑡 – τ 2)) = 0, is presented, which improves other conditions and an example is given to illustrate our result.

scholarly journals Some Remark on Oscillation of Second Order Impulsive Delay Dynamic Equations on Time Scales

2020 ◽  
Vol 76 (1) ◽  
pp. 115-126
Author(s):  
Gokula Nanda Chhatria
Keyword(s):  
Time Scales ◽  
Time Scale ◽  
Second Order ◽  
Dynamic Equations ◽  
Riccati Transformation ◽  
Transformation Technique ◽  
Oscillation Criteria ◽  
Delay Dynamic Equations ◽  
Impulsive Delay

AbstractThis article deals with the oscillation criteria for a very extensively studied second order impulsive delay dynamic equations on time scale by using the Riccati transformation technique. Some examples are given to show the effect of impulse and to illustrate our main results.

Kiguradze-type Oscillation Theorems for Second Order Superlinear Dynamic Equations on Time Scales

2011 ◽  
Vol 54 (4) ◽  
pp. 580-592 ◽  
Author(s):  
Jia Baoguo ◽  
Lynn Erbe ◽  
Allan Peterson
Keyword(s):  
Difference Equation ◽  
Dynamic Equation ◽  
Time Scale ◽  
Nonlinear Function ◽  
Second Order ◽  
Dynamic Equations ◽  
Coefficient Function ◽  
The Difference ◽  
Oscillation Theorems ◽  
Type Oscillation

AbstractConsider the second order superlinear dynamic equationwhere p ∈ C(, ℝ), is a time scale, ƒ : ℝ → ℝ is continuously differentiable and satisfies ƒ ′(x) > 0, and x ƒ (x) > 0 for x ≠ 0. Furthermore, f (x) also satisfies a superlinear condition, which includes the nonlinear function ƒ (x) = xα with α > 1, commonly known as the Emden–Fowler case. Here the coefficient function p(t) is allowed to be negative for arbitrarily large values of t. In addition to extending the result of Kiguradze for (∗) in the real case = ℝ, we obtain analogues in the difference equation and q-difference equation cases.

scholarly journals Oscillation Criteria for a Class of Second-Order Neutral Delay Dynamic Equations of Emden-Fowler Type

2011 ◽  
Vol 2011 ◽  
pp. 1-26 ◽  
Author(s):  
Zhenlai Han ◽  
Tongxing Li ◽  
Shurong Sun ◽  
Chao Zhang ◽  
Bangxian Han
Keyword(s):  
Time Scale ◽  
Second Order ◽  
Dynamic Equations ◽  
Neutral Delay ◽  
Oscillation Criteria ◽  
Delay Dynamic Equations ◽  
Positive Functions ◽  
Positive Integers

We establish some new oscillation criteria for the second-order neutral delay dynamic equations of Emden-Fowler type,[a(t)(x(t)+r(t)x(τ(t)))Δ]Δ+p(t)xγ(δ(t))=0,on a time scale unbounded above. Hereγ>0is a quotient of odd positive integers with a andpbeing real-valued positive functions defined on𝕋. Our results in this paper not only extend and improve the results in the literature but also correct an error in one of the references.

scholarly journals Amended Criteria of Oscillation for Nonlinear Functional Dynamic Equations of Second-Order

Mathematics ◽  
2021 ◽  
Vol 9 (11) ◽  
pp. 1191
Author(s):  
Taher S. Hassan ◽  
Rami Ahmad El-Nabulsi ◽  
Amir Abdel Menaem
Keyword(s):  
Time Scale ◽  
Averaging Method ◽  
Second Order ◽  
Dynamic Equations ◽  
Riccati Transformation ◽  
Nonlinear Functional ◽  
Oscillation Criteria ◽  
Arbitrary Time ◽  
Type Oscillation

In this paper, the sharp Hille-type oscillation criteria are proposed for a class of second-order nonlinear functional dynamic equations on an arbitrary time scale, by using the technique of Riccati transformation and integral averaging method. The obtained results demonstrate an improvement in Hille-type compared with the results reported in the literature. Some examples are provided to illustrate the significance of the obtained results.

Oscillation criteria for quasi-linear neutral delay dynamic equations on time scale

2016 ◽  
Vol 66 (1) ◽  
Author(s):  
Qiaoshun Yang ◽  
Zhiting Xu ◽  
Ping Long
Keyword(s):  
Dynamic Equation ◽  
Time Scale ◽  
Second Order ◽  
Dynamic Equations ◽  
Neutral Delay ◽  
Oscillation Criteria ◽  
Neutral Dynamic Equation ◽  
Delay Dynamic Equations

AbstractIn this paper, we consider the oscillation for the second-order quasi-linear neutral dynamic equationon time scale 𝕋, where

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