scholarly journals Stability, Boundedness, and Existence of Periodic Solutions to Certain Third-Order Delay Differential Equations with Multiple Deviating Arguments

2015 ◽  
Vol 2015 ◽  
pp. 1-12 ◽  
Author(s):  
A. T. Ademola ◽  
B. S. Ogundare ◽  
M. O. Ogundiran ◽  
O. A. Adesina
Keyword(s):  
Differential Equations ◽  
Nonlinear Differential Equations ◽  
Sufficient Conditions ◽  
Asymptotically Stable ◽  
Third Order ◽  
Deviating Arguments ◽  
Multiple Deviating Arguments ◽  
Lyapunov’S Second Method ◽  
Existence Of Periodic Solutions ◽  
Delay Differential

The behaviour of solutions for certain third-order nonlinear differential equations with multiple deviating arguments is considered. By employing Lyapunov’s second method, a complete Lyapunov functional is constructed and used to establish sufficient conditions that guarantee existence of unique solutions that are periodic, uniformly asymptotically stable, and uniformly ultimately bounded. Obtained results not only are new but also include many outstanding results in the literature. Finally, the correctness and effectiveness of the results are justified with examples.

scholarly journals Existence and uniqueness of a periodic solution to certain third order nonlinear delay differential equation with multiple deviating arguments

2013 ◽  
Vol 5 (2) ◽  
pp. 113-1 ◽  
Author(s):  
Adeleke Timothy Ademola
Keyword(s):  
Periodic Solution ◽  
Existence And Uniqueness ◽  
Sufficient Conditions ◽  
Third Order ◽  
Deviating Arguments ◽  
Multiple Deviating Arguments ◽  
Uniform Ultimate Boundedness ◽  
Lyapunov’S Second Method ◽  
Delay Differential ◽  
Nonlinear Delay Differential Equation

Abstract In this paper, we use Lyapunov’s second method, by constructing a complete Lyapunov functional, sufficient conditions which guarantee existence and uniqueness of a periodic solution, uniform asymptotic stability of the trivial solution and uniform ultimate boundedness of solutions of Eq. (2). New results are obtained and proved, an example is given to illustrate the theoretical analysis in the work and to test the effectiveness of the method employed. The results obtained in this investigation extend many existing and exciting results on nonlinear third order delay differential equations.

scholarly journals Existence of Periodic Solutions to Nonlinear Differential Equations of Third Order with Multiple Deviating Arguments

2012 ◽  
Vol 2012 ◽  
pp. 1-13 ◽  
Author(s):  
Cemil Tunç
Keyword(s):  
Periodic Solutions ◽  
Lyapunov Functional ◽  
Nonlinear Differential Equations ◽  
Sufficient Conditions ◽  
Functional Approach ◽  
Third Order ◽  
Deviating Arguments ◽  
The Third ◽  
Multiple Deviating Arguments ◽  
Existence Of Periodic Solutions

We establish certain new sufficient conditions which guarantee the existence of periodic solutions for a nonlinear differential equation of the third order with multiple deviating arguments. Using the Lyapunov functional approach, we prove a specific theorem and provide an example to illustrate the theoretical analysis in this work and the effectiveness of the method utilized here.

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.

scholarly journals Qualitative Behaviors of Functional Differential Equations of Third Order with Multiple Deviating Arguments

2012 ◽  
Vol 2012 ◽  
pp. 1-12 ◽  
Author(s):  
Cemil Tunç
Keyword(s):  
Differential Equations ◽  
Functional Differential Equations ◽  
Sufficient Conditions ◽  
Functional Approach ◽  
Third Order ◽  
Deviating Arguments ◽  
The Third ◽  
Multiple Deviating Arguments ◽  
Functional Differential ◽  
Made In

This paper considers nonautonomous functional differential equations of the third order with multiple constant deviating arguments. Using the Lyapunov-Krasovskii functional approach, we find certain sufficient conditions for the solutions to be stable and bounded. We give an example to illustrate the theoretical analysis made in this work and to show the effectiveness of the method utilized here.

On solutions of third order nonlinear differential equations

2006 ◽  
Vol 4 (1) ◽  
pp. 46-63 ◽  
Author(s):  
Ivan Mojsej ◽  
Ján Ohriska
Keyword(s):  
Differential Equations ◽  
Nonlinear Equations ◽  
Nonlinear Differential Equations ◽  
Asymptotic Properties ◽  
Property A ◽  
Comparison Result ◽  
Third Order ◽  
Deviating Arguments ◽  
Deviating Argument ◽  
The Third

AbstractThe aim of our paper is to study oscillatory and asymptotic properties of solutions of nonlinear differential equations of the third order with deviating argument. In particular, we prove a comparison theorem for properties A and B as well as a comparison result on property A between nonlinear equations with and without deviating arguments. Our assumptions on nonlinearity f are related to its behavior only in a neighbourhood of zero and/or of infinity.

Oscillation criteria for third-order nonlinear differential equations

2008 ◽  
Vol 58 (2) ◽  
Author(s):  
B. Baculíková ◽  
E. Elabbasy ◽  
S. Saker ◽  
J. Džurina
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Order Differential Equation ◽  
Nonlinear Differential Equations ◽  
Sufficient Conditions ◽  
Third Order ◽  
Oscillation Criteria ◽  
The Third ◽  
Third Order Differential Equation ◽  
Oscillation Properties

AbstractIn this paper, we are concerned with the oscillation properties of the third order differential equation $$ \left( {b(t) \left( {[a(t)x'(t)'} \right)^\gamma } \right)^\prime + q(t)x^\gamma (t) = 0, \gamma > 0 $$. Some new sufficient conditions which insure that every solution oscillates or converges to zero are established. The obtained results extend the results known in the literature for γ = 1. Some examples are considered to illustrate our main results.

scholarly journals On the asymptotic behavior of solutions of certain third-order nonlinear differential equations

2005 ◽  
Vol 2005 (1) ◽  
pp. 29-35 ◽  
Author(s):  
Cemil Tunç
Keyword(s):  
Differential Equation ◽  
Asymptotic Behavior ◽  
Differential Equations ◽  
Nonlinear Differential Equation ◽  
Nonlinear Differential Equations ◽  
Sufficient Conditions ◽  
Asymptotic Behavior Of Solutions ◽  
Third Order ◽  
The Third ◽  
All Solutions

We establish sufficient conditions under which all solutions of the third-order nonlinear differential equation x ⃛+ψ(x,x˙,x¨)x¨+f(x,x˙)=p(t,x,x˙,x¨) are bounded and converge to zero as t→∞.

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