scholarly journals Asymptotic Dichotomy in a Class of Fourth-Order Nonlinear Delay Differential Equations with Damping

2009 ◽  
Vol 2009 ◽  
pp. 1-7 ◽  
Author(s):  
Chengmin Hou ◽  
Sui Sun Cheng
Keyword(s):  
Differential Equations ◽  
Fourth Order ◽  
Delay Differential Equations ◽  
Third Order ◽  
All Solutions ◽  
Nonlinear Delay Differential Equations ◽  
Linear Differential ◽  
Delay Differential ◽  
Nonlinear Delay Differential Equation ◽  
Nonlinear Delay

All solutions of a fourth-order nonlinear delay differential equation are shown to converge to zero or to oscillate. Novel Riccati type techniques involving third-order linear differential equations are employed. Implications in the deflection of elastic horizontal beams are also indicated.

scholarly journals New Results for Kneser Solutions of Third-Order Nonlinear Neutral Differential Equations

Mathematics ◽  
2020 ◽  
Vol 8 (5) ◽  
pp. 686 ◽  
Author(s):  
Osama Moaaz ◽  
Belgees Qaraad ◽  
Rami Ahmad El-Nabulsi ◽  
Omar Bazighifan
Keyword(s):  
Differential Equations ◽  
Nonlinear Equation ◽  
Delay Differential Equations ◽  
Third Order ◽  
Neutral Differential Equations ◽  
All Solutions ◽  
Nonlinear Delay Differential Equations ◽  
Delay Differential ◽  
New Criteria ◽  
Nonlinear Delay

In this paper, we consider a certain class of third-order nonlinear delay differential equations r w ″ α ′ v + q v x β ς v = 0 , for v ≥ v 0 , where w v = x v + p v x ϑ v . We obtain new criteria for oscillation of all solutions of this nonlinear equation. Our results complement and improve some previous results in the literature. An example is considered to illustrate our main results.

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