scholarly journals Oscillatory behavior of third-order nonlinear differential equations with mixed neutral terms

2021 ◽  
pp. 1-12
Author(s):  
Said GRACE ◽  
John R. GRAEF ◽  
Ercan TUNC
Keyword(s):  
Differential Equations ◽  
Nonlinear Differential Equations ◽  
Oscillatory Behavior ◽  
Third Order

Asymptotics for third-order nonlinear differential equations: Non-oscillatory and oscillatory cases

2021 ◽  
pp. 1-19
Author(s):  
Calogero Vetro ◽  
Dariusz Wardowski
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Order Differential Equation ◽  
Nonlinear Differential Equations ◽  
Oscillatory Behavior ◽  
Third Order ◽  
First Order ◽  
Third Order Differential Equation ◽  
Comparison Technique ◽  
First Order Differential Equations

We discuss a third-order differential equation, involving a general form of nonlinearity. We obtain results describing how suitable coefficient functions determine the asymptotic and (non-)oscillatory behavior of solutions. We use comparison technique with first-order differential equations together with the Kusano–Naito’s and Philos’ approaches.

scholarly journals Oscillatory behavior of nonlinear differential equations with deviating arguments

1985 ◽  
Vol 31 (1) ◽  
pp. 127-136 ◽  
Author(s):  
S.R. Grace ◽  
B.S. Lalli
Keyword(s):  
Differential Equations ◽  
Nonlinear Differential Equations ◽  
Oscillatory Behavior ◽  
Deviating Arguments ◽  
Oscillation Criteria ◽  
Image Position

New oscillation criteria for nonlinear differential equations with deviating arguments of the formn even, are established.

scholarly journals Asymptotic Dichotomy in a Class of Third-Order Nonlinear Differential Equations with Impulses

2010 ◽  
Vol 2010 ◽  
pp. 1-20 ◽  
Author(s):  
Kun-Wen Wen ◽  
Gen-Qiang Wang ◽  
Sui Sun Cheng
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Nonlinear Differential Equation ◽  
Nonlinear Differential Equations ◽  
Functional Differential Equations ◽  
Higher Order ◽  
Third Order ◽  
Order Nonlinear Differential Equation ◽  
Functional Differential

Solutions of quite a few higher-order delay functional differential equations oscillate or converge to zero. In this paper, we obtain several such dichotomous criteria for a class of third-order nonlinear differential equation with impulses.

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