A Generalized Fourier Method for the System of First-Order Differential Equations with an Involution and a Group of Operators

2018 ◽  
Vol 54 (2) ◽  
pp. 277-281 ◽  
Author(s):  
A. G. Baskakov ◽  
N. B. Uskova
Keyword(s):  
Differential Equations ◽  
Fourier Method ◽  
First Order ◽  
Generalized Fourier Method ◽  
First Order Differential Equations

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.

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