Specific Asymptotic Stability of Solutions to a Linear Homogeneous Volterra Integro-Differential Equation of the Fourth Order

2021 ◽  
Vol 76 (1) ◽  
pp. 22-28
Author(s):  
S. Iskandarov ◽  
E. A. Komartsova
Keyword(s):  
Differential Equation ◽  
Asymptotic Stability ◽  
Fourth Order ◽  
Stability Of Solutions ◽  
Integro Differential Equation

scholarly journals ON SPECIFIC ASYMPTOTIC STABILITY SOLUTIONS OF A LINEAR HOMOGENEOUS WELTERER INTEGRO-DIFFERENTIAL EQUATION OF THE FOURTH ORDER

2021 ◽  
pp. 110-117
Author(s):  
Z. A. Japarova
Keyword(s):  
Differential Equation ◽  
Asymptotic Stability ◽  
Fourth Order ◽  
Order Differential Equation ◽  
Sufficient Conditions ◽  
Third Order ◽  
Volterra Type ◽  
Integro Differential Equation ◽  
The Third ◽  
Fourth Order Differential Equation

Specific sufficient conditions for the asymptotic stability of a linear homogeneous fourthorder integro-differential equation of the Volterra type are established in the case when all nonzero solutions of the corresponding fourth-order differential equation do not have the property of asymptotic stability of the solutions. In this paper, we obtain estimates on the semiaxis of the solution and the derivative up to the 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.

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