scholarly journals On global asymptotic stability of solutions of a system of ordinary differential equations

2017 ◽  
Author(s):  
M. Yu. Filimonov
Keyword(s):  
Asymptotic Stability ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Global Asymptotic Stability ◽  
Stability Of Solutions

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.

Bounded and Vanishing at Infinity Solutions of Nonlinear Differential Systems

2009 ◽  
Vol 16 (4) ◽  
pp. 711-724
Author(s):  
Ivan Kiguradze
Keyword(s):  
Asymptotic Stability ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Global Asymptotic Stability ◽  
Trivial Solution ◽  
Well Posedness ◽  
Bounded Solutions ◽  
Differential Systems ◽  
Nonlinear Differential Systems

Abstract For systems of nonlinear nonautonomous ordinary differential equations, the conditions, optimal in a certain sense, are established, which guarantee the solvability and well-posedness of the problem on bounded solutions, the vanishing at infinity of all bounded solutions and the global asymptotic stability of a trivial solution.

Stability of Solutions of Ordinary Differential Equations with Respect to a Closed Set

1968 ◽  
Vol 20 ◽  
pp. 720-726
Author(s):  
T. G. Hallam ◽  
V. Komkov
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Compact Set ◽  
Stability Of Solutions ◽  
Closed Set ◽  
The Stability ◽  
Stability Results

The stability of the solutions of an ordinary differential equation will be discussed here. The purpose of this note is to compare the stability results which are valid with respect to a compact set and the stability results valid with respect to an unbounded set. The stability of sets is a generalization of stability in the sense of Liapunov and has been discussed by LaSalle (5; 6), LaSalle and Lefschetz (7, p. 58), and Yoshizawa (8; 9; 10).

scholarly journals The Asymptotic Behaviours of a Class of Neutral Delay Fractional-Order Pantograph Differential Equations

2017 ◽  
Vol 2017 ◽  
pp. 1-6
Author(s):  
Baojun Miao ◽  
Xuechen Li
Keyword(s):  
Asymptotic Stability ◽  
Differential Equations ◽  
Fractional Calculus ◽  
Fractional Order ◽  
Asymptotic Estimates ◽  
Stability Of Solutions ◽  
Neutral Delay ◽  
Estimates Of Solutions ◽  
Fractional Delay ◽  
Asymptotic Behaviours

By using fractional calculus and the summation by parts formula in this paper, the asymptotic behaviours of solutions of nonlinear neutral fractional delay pantograph equations with continuous arguments are investigated. The asymptotic estimates of solutions for the equation are obtained, which may imply asymptotic stability of solutions. In the end, a particular case is provided to illustrate the main result and the speed of the convergence of the obtained solutions.

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