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.

scholarly journals Oscillation for Forced Second-Order Impulsive Nonlinear Dynamic Equations on Time Scales

2019 ◽  
Vol 2019 ◽  
pp. 1-7
Author(s):  
Mugen Huang ◽  
Kunwen Wen
Keyword(s):  
Time Scales ◽  
Impulsive Differential Equations ◽  
Second Order ◽  
Dynamic Equations ◽  
Riccati Transformation ◽  
Transformation Technique ◽  
Social Phenomena ◽  
Nonlinear Dynamic Equations ◽  
Interval Oscillation ◽  
Positive Axis

As the unification and development of impulsive differential equations and difference equations, impulsive dynamic equations on time scales are a powerful tool to simulate the natural and social phenomena. In this paper, we study the interval oscillation of a type of forced second-order nonlinear impulsive dynamic equations with changing signs coefficients. By using the Riccati transformation technique, we obtain some new interval oscillation criteria, based only on information of a sequence of subintervals of positive axis. In addition, we provide an example to illustrate the use of our oscillatory 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 Interval Oscillation Criteria of Second-Order Nonlinear Dynamic Equations on Time Scales

2012 ◽  
Vol 2012 ◽  
pp. 1-16 ◽  
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 ◽  
Interval Oscillation

Using functions in some function classes and a generalized Riccati technique, we establish interval oscillation criteria for second-order nonlinear dynamic equations on time scales of the form(p(t)ψ(x(t))xΔ(t))Δ+f(t,x(σ(t)))=0. The obtained interval oscillation criteria can be applied to equations with a forcing term. An example is included to show the significance of the results.

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 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.

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.

scholarly journals Oscillation Criteria for Second-Order Nonlinear Dynamic Equations on Time Scales

2012 ◽  
Vol 2012 ◽  
pp. 1-20 ◽  
Author(s):  
Shao-Yan Zhang ◽  
Qi-Ru Wang
Keyword(s):  
Time Scales ◽  
Nonlinear Dynamic ◽  
Second Order ◽  
Dynamic Equations ◽  
Riccati Technique ◽  
Oscillation Criteria ◽  
Nonlinear Dynamic Equations ◽  
Generalized Riccati Technique ◽  
Averaging Techniques

This paper is concerned with oscillation of second-order nonlinear dynamic equations of the form on time scales. By using a generalized Riccati technique and integral averaging techniques, we establish new oscillation criteria which handle some cases not covered by known criteria.

scholarly journals Oscillation Criteria for Nonlinear Third-Order Neutral Dynamic Equations with Damping on Time Scales

2017 ◽  
Vol 2017 ◽  
pp. 1-8
Author(s):  
Yang-Cong Qiu ◽  
Akbar Zada ◽  
Haiyong Qin ◽  
Tongxing Li
Keyword(s):  
Time Scales ◽  
Nonlinear Dynamic ◽  
Dynamic Equations ◽  
Riccati Transformation ◽  
Damping Term ◽  
Third Order ◽  
Oscillation Criteria ◽  
Nonlinear Dynamic Equations ◽  
Neutral Dynamic Equations

We establish several oscillation criteria for a class of third-order nonlinear dynamic equations with a damping term and a nonpositive neutral coefficient by using the Riccati transformation. Two illustrative examples are presented to show the significance of the results obtained.

scholarly journals Interval Oscillation Criteria for Second-Order Forced Functional Dynamic Equations on Time Scales

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Shao-Yan Zhang ◽  
Qi-Ru Wang
Keyword(s):  
Time Scales ◽  
Second Order ◽  
Dynamic Equations ◽  
Riccati Technique ◽  
Oscillation Criteria ◽  
Generalized Riccati Technique ◽  
Interval Oscillation ◽  
Averaging Techniques

This paper is concerned with oscillation of second-order forced functional dynamic equations of the form(r(t)(xΔ(t))γ)Δ+∑i=0n‍qi(t)|x(δi(t))|αisgn  x(δi(t))=e(t)on time scales. By using a generalized Riccati technique and integral averaging techniques, we establish new oscillation criteria which handle some cases not covered by known criteria.

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