scholarly journals New oscillation criteria for second-order neutral dynamic equations on time scales via Riccati substitution

2012 ◽  
Vol 42 (1) ◽  
pp. 77-98 ◽  
Author(s):  
S. H. Saker ◽  
Donal O’Regan
Keyword(s):  
Time Scales ◽  
Second Order ◽  
Dynamic Equations ◽  
Oscillation Criteria ◽  
Riccati Substitution ◽  
Neutral Dynamic Equations

scholarly journals A note on "oscillation criteria for second-order nonlinear neutral dynamic equations on time scales

2015 ◽  
Vol 46 (4) ◽  
pp. 435-439
Author(s):  
Hassan Ahmed Hassan Agwa ◽  
Ahmed Mohamed Mohamed Khodier ◽  
Mahmoud Haman Osman Salm
Keyword(s):  
Time Scales ◽  
Second Order ◽  
Dynamic Equations ◽  
Oscillation Criteria ◽  
Counter Example ◽  
Correct Formula ◽  
Neutral Dynamic Equations

In this work, we give a counter example for the main result of the paper \small[Tamkang J. of Math., 43 (1)(2012), 109--122.] and we give the correct formula for some theorems given in their work.

scholarly journals Oscillation criteria for second order nonlinear neutral dynamic equations on time scales

2012 ◽  
Vol 43 (1) ◽  
pp. 109-122
Author(s):  
E. Thandapani ◽  
V. Piramanantham
Keyword(s):  
Time Scales ◽  
Second Order ◽  
Dynamic Equations ◽  
Neutral Delay ◽  
Oscillation Criteria ◽  
Delay Dynamic Equations ◽  
Neutral Dynamic Equations

In this paper the authors established some new oscillation criteria for the second order nonlinear neutral delay dynamic equations on time scales. Examples illustrating the main results are given.

scholarly journals Oscillation and nonoscillation theorems of neutral dynamic equations on time scales

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Yong Zhou ◽  
Ahmed Alsaedi ◽  
Bashir Ahmad
Keyword(s):  
Time Scales ◽  
Dynamic Equation ◽  
Dynamic Equations ◽  
Nonoscillatory Solutions ◽  
Oscillation Criteria ◽  
Neutral Dynamic Equation ◽  
The Given ◽  
Neutral Dynamic Equations ◽  
Oscillation And Nonoscillation

Abstract We present the oscillation criteria for the following neutral dynamic equation on time scales: $$ \bigl(y(t)-C(t)y(t-\zeta )\bigr)^{\Delta }+P(t)y(t-\eta )-Q(t)y(t-\delta )=0, \quad t\in {\mathbb{T}}, $$ ( y ( t ) − C ( t ) y ( t − ζ ) ) Δ + P ( t ) y ( t − η ) − Q ( t ) y ( t − δ ) = 0 , t ∈ T , where $C, P, Q\in C_{\mathit{rd}}([t_{0},\infty ),{\mathbb{R}}^{+})$ C , P , Q ∈ C rd ( [ t 0 , ∞ ) , R + ) , ${\mathbb{R}} ^{+}=[0,\infty )$ R + = [ 0 , ∞ ) , $\gamma , \eta , \delta \in {\mathbb{T}}$ γ , η , δ ∈ T and $\gamma >0$ γ > 0 , $\eta >\delta \geq 0$ η > δ ≥ 0 . New conditions for the existence of nonoscillatory solutions of the given equation are also obtained.

scholarly journals Oscillation criteria for second-order dynamic equations on time scales

2014 ◽  
Vol 31 ◽  
pp. 34-40 ◽  
Author(s):  
Ravi P. Agarwal ◽  
Martin Bohner ◽  
Tongxing Li ◽  
Chenghui Zhang
Keyword(s):  
Time Scales ◽  
Second Order ◽  
Dynamic Equations ◽  
Oscillation Criteria

scholarly journals New Oscillation Results of Second-Order Damped Dynamic Equations withp-Laplacian on Time Scales

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
Yang-Cong Qiu ◽  
Qi-Ru Wang
Keyword(s):  
Time Scales ◽  
Dynamic Equation ◽  
Second Order ◽  
Dynamic Equations ◽  
Coefficient Function ◽  
Riccati Technique ◽  
Oscillation Criteria ◽  
Function Classes ◽  
Generalized Riccati Technique

By employing a generalized Riccati technique and functions in some function classes for integral averaging, we derive new oscillation criteria of second-order damped dynamic equation withp-Laplacian on time scales of the form(rtφγ(xΔ(t)))Δ+ptφγ(xΔ(t))+f(t,x(g(t)))=0, where the coefficient functionp(t)may change sign. Two examples are given to demonstrate the obtained results.

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