On Global Asymptotic Stability of Solutions of Differential Equations

1962 ◽  
Vol 104 (1) ◽  
pp. 154 ◽  
Author(s):  
Philip Hartman ◽  
Czeslaw Olech
Keyword(s):  
Asymptotic Stability ◽  
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.

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.

scholarly journals Global asymptotic stability of differential equations in the plane

1991 ◽  
Vol 91 (2) ◽  
pp. 327-335 ◽  
Author(s):  
Armengol Gasull ◽  
Jaume Llibre ◽  
Jorge Sotomayor
Keyword(s):  
Asymptotic Stability ◽  
Differential Equations ◽  
Global Asymptotic Stability
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