scholarly journals Asymptotic Behaviour of Solutions of Certain Third Order Nonlinear Differential Equations via Phase Portrait Analysis

2016 ◽  
Vol 07 (18) ◽  
pp. 2324-2335 ◽  
Author(s):  
Roseline Ngozi Okereke ◽  
Sadik Olaniyi Maliki
Keyword(s):  
Differential Equations ◽  
Asymptotic Behaviour ◽  
Phase Portrait ◽  
Nonlinear Differential Equations ◽  
Third Order ◽  
Asymptotic Behaviour Of Solutions ◽  
Phase Portrait Analysis

scholarly journals On asymptotic equivalence of nth order nonlinear differential equations

2015 ◽  
Vol 63 (1) ◽  
pp. 31-38
Author(s):  
Irina Astashova
Keyword(s):  
Differential Equations ◽  
Asymptotic Behaviour ◽  
Nonlinear Differential Equations ◽  
Asymptotic Equivalence ◽  
Right Hand ◽  
Asymptotic Behaviour Of Solutions

Abstract This paper is devoted to the problem of asymptotic equivalence of nth order differential equations with exponentially equivalent right-hand sides. With the help of this result asymptotic behaviour of solutions to nonhomogeneous differential equations is described

Asymptotic behaviour of solutions of some general nonlinear differential equations and integral inequalities

1984 ◽  
Vol 98 (1-2) ◽  
pp. 49-67 ◽  
Author(s):  
Paul R. Beesack
Keyword(s):  
Differential Equations ◽  
Asymptotic Behaviour ◽  
Nonlinear Differential Equations ◽  
Upper Bounds ◽  
Integral Inequalities ◽  
Asymptotic Behaviour Of Solutions ◽  
Type Integral ◽  
Image Position ◽  
Complex Valued

SynopsisWe deal with the asymptotic behaviour, as t→∞, of complex-valued solutions of nonlinear differential equationsUpper bounds for ∣x(l)(t)∣, 0≦j≦n, are obtained by obtaining upper bounds for solutions u(t) of Bihari-type integral inequalities of the form

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 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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