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 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 Stability and Uniform Boundedness in Multidelay Functional Differential Equations of Third Order

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Cemil Tunç ◽  
Melek Gözen
Keyword(s):  
Differential Equation ◽  
Functional Differential Equations ◽  
Sufficient Conditions ◽  
Uniform Boundedness ◽  
Functional Approach ◽  
Third Order ◽  
Deviating Arguments ◽  
The Third ◽  
Multiple Deviating Arguments ◽  
Functional Differential

We consider a nonautonomous functional differential equation of the third order with multiple deviating arguments. Using the Lyapunov-Krasovskiì functional approach, we give certain sufficient conditions to guarantee the asymptotic stability and uniform boundedness of the solutions.

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 Oscillation Criteria of Certain Third-Order Differential Equation with Piecewise Constant Argument

2012 ◽  
Vol 2012 ◽  
pp. 1-18 ◽  
Author(s):  
Haihua Liang ◽  
Gen-qiang Wang
Keyword(s):  
Differential Equation ◽  
Order Differential Equation ◽  
Sufficient Conditions ◽  
Third Order ◽  
Piecewise Constant ◽  
Piecewise Constant Argument ◽  
Delay Differential ◽  
Nonlinear Delay Differential Equation ◽  
Nonlinear Delay ◽  
Constant Argument

We study the oscillation and asymptotic behavior of third-order nonlinear delay differential equation with piecewise constant argument of the form(r2(t)(r1(t)x'(t))')'+p(t)x'(t)+f(t,x([t]))=0. We establish several sufficient conditions which insure that any solution of this equation oscillates or converges to zero. Some examples are given to illustrate the importance of our results.

Stability and boundedness of solutions of a certain n-dimensional nonlinear delay differential system of third-order

2015 ◽  
Vol 0 (0) ◽  
Author(s):  
Ayman M. Mahmoud ◽  
Cemil Tunç
Keyword(s):  
Sufficient Conditions ◽  
Uniform Boundedness ◽  
Zero Solution ◽  
Third Order ◽  
All Solutions ◽  
Uniform Ultimate Boundedness ◽  
Delay Differential System ◽  
Nonlinear Vector ◽  
Delay Differential ◽  
Nonlinear Delay

AbstractIn this paper, by defining Lyapunov functionals, we investigate proper sufficient conditions for the uniform stability of the zero solution, and also for the uniform boundedness and uniform ultimate boundedness of all solutions of a certain third-order nonlinear vector delay differential equation of the type

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.

scholarly journals Existence and Uniqueness of Solutions to Third-Order Boundary Value Problems

2021 ◽  
Vol 22 (2) ◽  
pp. 221-240
Author(s):  
S. S. Almuthaybiri ◽  
J. M. Jonnalagadda ◽  
C. C. Tisdell
Keyword(s):  
Fixed Point ◽  
Boundary Value Problems ◽  
Existence And Uniqueness ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Uniqueness Of Solutions ◽  
Third Order ◽  
Fixed Point Methods ◽  
Bounded Sets

The purpose of this research is to connect fixed point methods with certain third-order boundary value problems in new and interesting ways. Our strategy involves an analysis of the problem under consideration within closed and bounded sets. We develop sufficient conditions under which the associated mappings will be contractive and invariant in these sets, which generates new advances concerning the existence, uniqueness and approximation of solutions.

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