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.

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 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 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.

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 Kamenev-Type Oscillation Criteria of Second-Order Nonlinear Dynamic Equations on Time Scales

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
Yang-Cong Qiu ◽  
Qi-Ru Wang
Keyword(s):  
Time Scales ◽  
Nonlinear Dynamic ◽  
Second Order ◽  
Dynamic Equations ◽  
Riccati Technique ◽  
Oscillation Criteria ◽  
Function Classes ◽  
Nonlinear Dynamic Equations ◽  
Generalized Riccati Technique ◽  
Type Oscillation

Using functions from some function classes and a generalized Riccati technique, we establish Kamenev-type oscillation criteria for second-order nonlinear dynamic equations on time scales of the form(p(t)ψ(x(t))k∘xΔ(t))Δ+f(t,x(σ(t)))=0. Two examples are included to show the significance of the results.

Oscillation criteria for higher order nonlinear delay dynamic equations on time scales

2016 ◽  
Vol 66 (3) ◽  
Author(s):  
Xin Wu ◽  
Taixiang Sun
Keyword(s):  
Time Scales ◽  
Dynamic Equation ◽  
Time Scale ◽  
Higher Order ◽  
Dynamic Equations ◽  
Oscillation Criteria ◽  
Arbitrary Time ◽  
Delay Dynamic Equation ◽  
Delay Dynamic Equations ◽  
Nonlinear Delay

AbstractIn this paper, we study the oscillation criteria of the following higher order nonlinear delay dynamic equationon an arbitrary time scalewith

scholarly journals Oscillation Theorems for Second-Order Half-Linear Neutral Delay Dynamic Equations with Damping on Time Scales

2014 ◽  
Vol 2014 ◽  
pp. 1-12
Author(s):  
Quanxin Zhang ◽  
Shouhua Liu
Keyword(s):  
Time Scales ◽  
Second Order ◽  
Dynamic Equations ◽  
Riccati Transformation ◽  
Neutral Delay ◽  
Oscillation Criteria ◽  
Generalized Riccati Transformation ◽  
Delay Dynamic Equations ◽  
Inequality Technique ◽  
Oscillation Theorems

We establish the oscillation criteria of Philos type for second-order half-linear neutral delay dynamic equations with damping on time scales by the generalized Riccati transformation and inequality technique. Our results are new even in the continuous and the discrete cases.

New Kamenev-type oscillation criteria for second-order nonlinear advanced dynamic equations

2013 ◽  
Vol 225 ◽  
pp. 822-828 ◽  
Author(s):  
Ravi P. Agarwal ◽  
Chenghui Zhang ◽  
Tongxing Li
Keyword(s):  
Second Order ◽  
Dynamic Equations ◽  
Oscillation Criteria ◽  
Type Oscillation

scholarly journals Philos-Type Oscillation Criteria for Second Order Half-Linear Dynamic Equations on Time Scales

2007 ◽  
Vol 37 (4) ◽  
pp. 1085-1104 ◽  
Author(s):  
Ravi P. Agarwal ◽  
Donal O'Regan ◽  
S.H. Saker
Keyword(s):  
Time Scales ◽  
Second Order ◽  
Dynamic Equations ◽  
Oscillation Criteria ◽  
Linear Dynamic ◽  
Type Oscillation

scholarly journals Interval Oscillation Criteria for Second-Order Nonlinear Forced Dynamic Equations with Damping on Time Scales

2013 ◽  
Vol 2013 ◽  
pp. 1-11
Author(s):  
Yibing Sun ◽  
Zhenlai Han ◽  
Shurong Sun ◽  
Chao Zhang
Keyword(s):  
Positive Integer ◽  
Time Scales ◽  
Second Order ◽  
Dynamic Equations ◽  
Riccati Transformation ◽  
Transformation Technique ◽  
Oscillation Criteria ◽  
Nonlinear Dynamic Equations ◽  
Interval Oscillation ◽  
Forced Term

By using the Riccati transformation technique and constructing a class of Philos-type functions on time scales, we establish some new interval oscillation criteria for the second-order damped nonlinear dynamic equations with forced term of the form(r(t)xΔ(t))Δ+p(t)xΔσ(t)+q(t)(xσ(t))α=F(t,xσ(t))on a time scale𝕋which is unbounded, whereαis a quotient of odd positive integer. Our results in this paper extend and improve some known results. Some examples are given here to illustrate our main results.

Sign in / Sign up

Export Citation Format

Share Document