scholarly journals New Oscillation Theorems for Second-Order Differential Equations with Canonical and Non-Canonical Operator via Riccati Transformation

Mathematics ◽  
2021 ◽  
Vol 9 (10) ◽  
pp. 1111
Author(s):  
Shyam Sundar Santra ◽  
Abhay Kumar Sethi ◽  
Osama Moaaz ◽  
Khaled Mohamed Khedher ◽  
Shao-Wen Yao
Keyword(s):  
Differential Equations ◽  
Delay Differential Equations ◽  
Second Order ◽  
Riccati Transformation ◽  
Neutral Delay ◽  
Canonical Operator ◽  
Second Order Differential Equations ◽  
Neutral Delay Differential Equations ◽  
Delay Differential ◽  
Oscillation Theorems

In this work, we prove some new oscillation theorems for second-order neutral delay differential equations of the form (a(ξ)((v(ξ)+b(ξ)v(ϑ(ξ)))′))′+c(ξ)G1(v(κ(ξ)))+d(ξ)G2(v(ς(ξ)))=0 under canonical and non-canonical operators, that is, ∫ξ0∞dξa(ξ)=∞ and ∫ξ0∞dξa(ξ)<∞. We use the Riccati transformation to prove our main results. Furthermore, some examples are provided to show the effectiveness and feasibility of the main results.

scholarly journals Oscillation Theorems for Second-Order Nonlinear Neutral Delay Differential Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-5 ◽  
Author(s):  
Tongxing Li ◽  
Yuriy V. Rogovchenko
Keyword(s):  
Differential Equations ◽  
Delay Differential Equations ◽  
Oscillatory Behavior ◽  
Second Order ◽  
Neutral Delay ◽  
Neutral Delay Differential Equations ◽  
Delay Differential ◽  
Oscillation Theorems

We analyze the oscillatory behavior of solutions to a class of second-order nonlinear neutral delay differential equations. Our theorems improve a number of related results reported in the literature.

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