Global asymptotic stability of certain third-order nonlinear differential equations

2013 ◽  
Vol 36 (14) ◽  
pp. 1845-1850 ◽  
Author(s):  
Lijuan Zhang ◽  
Lixin Yu
Keyword(s):  
Asymptotic Stability ◽  
Differential Equations ◽  
Global Asymptotic Stability ◽  
Nonlinear Differential Equations ◽  
Third Order

On Stability of Solutions of Certain Differential Equations of the Third Order

1967 ◽  
Vol 10 (5) ◽  
pp. 681-688 ◽  
Author(s):  
B.S. Lalli
Keyword(s):  
Differential Equation ◽  
Asymptotic Stability ◽  
Lyapunov Function ◽  
Differential Equations ◽  
Global Asymptotic Stability ◽  
Sufficient Conditions ◽  
Stability Of Solutions ◽  
Third Order ◽  
The Third ◽  
Image Position

The purpose of this paper is to obtain a set of sufficient conditions for “global asymptotic stability” of the trivial solution x = 0 of the differential equation1.1using a Lyapunov function which is substantially different from similar functions used in [2], [3] and [4], for similar differential equations. The functions f1, f2 and f3 are real - valued and are smooth enough to ensure the existence of the solutions of (1.1) on [0, ∞). The dot indicates differentiation with respect to t. We are taking a and b to be some positive parameters.

scholarly journals On Stability of Certain Class of 3-Rd Order Nonlinear Control Systems

2014 ◽  
Vol 22 (35) ◽  
pp. 39-47
Author(s):  
Oleg Palumbíny ◽  
Martin Neštický
Keyword(s):  
Asymptotic Stability ◽  
Differential Equations ◽  
Nonlinear Control ◽  
Control Systems ◽  
Nonlinear Differential Equations ◽  
Nonlinear Control Systems ◽  
Third Order

AbstractThe paper deals with a certain class of nonautonomous ordinary third-order nonlinear differential equations L3y=f(t,L0y,L1y,L2y) with quasi-derivatives. A criterion of asymptotic stability in Liapunov sense as well as a criterion of instability in Liapunov sense is derived. The results are illustrated by two examples.

scholarly journals Stability of the solutions of nonlinear third order differential equations with multiple deviating arguments

2016 ◽  
Vol 8 (1) ◽  
pp. 150-165 ◽  
Author(s):  
Moussadek Remili ◽  
Lynda Damerdji Oudjedi
Keyword(s):  
Asymptotic Stability ◽  
Differential Equations ◽  
Lyapunov Functional ◽  
Nonlinear Differential Equations ◽  
Stability Of Solutions ◽  
Third Order ◽  
Deviating Arguments ◽  
Multiple Deviating Arguments

Abstract In this paper, with use of Lyapunov functional, we investigate asymptotic stability of solutions of some nonlinear differential equations of third order with delay. Our results include and improve some well-known results in the literature.

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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