scholarly journals On the uniform boundedness of solutions of Lienard type equations with multiple deviating arguments

2011 ◽  
Vol 27 (2) ◽  
pp. 269-275
Author(s):  
CEMIL TUNC ◽  
Keyword(s):  
Lyapunov Functional ◽  
Sufficient Conditions ◽  
Type Equation ◽  
Uniform Boundedness ◽  
Functional Approach ◽  
Boundedness Of Solutions ◽  
Deviating Arguments ◽  
Multiple Deviating Arguments ◽  
Multiple Variable ◽  
Liénard Type Equation

This paper considers a Lienard type equation with multiple variable deviating arguments. We find some sufficient conditions for the solution of this equation to be uniform bounded by utilizing Lyapunov functional approach. An example is also given to show the effectiveness of our result.

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 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 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 and boundedness to certain differential equations of fourth order with multiple delays

Filomat ◽  
2014 ◽  
Vol 28 (5) ◽  
pp. 1049-1058 ◽  
Author(s):  
Erdal Korkmaz ◽  
Cemil Tunc
Keyword(s):  
Asymptotic Stability ◽  
Differential Equations ◽  
Fourth Order ◽  
Functional Differential Equations ◽  
Sufficient Conditions ◽  
Functional Approach ◽  
Multiple Delays ◽  
Boundedness Of Solutions ◽  
Functional Differential ◽  
The Stability

In this paper, we give sufficient conditions to guarantee the asymptotic stability and boundedness of solutions to a kind of fourth-order functional differential equations with multiple delays. By using the Lyapunov-Krasovskii functional approach, we establish two new results on the stability and boundedness of solutions, which include and improve some related results in the literature.

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 Instability in Multi Delay Functional Differential Equations of Fourth Order

2015 ◽  
Vol 55 (1) ◽  
pp. 189-198
Author(s):  
Cemil Tunç
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Fourth Order ◽  
Functional Differential Equations ◽  
Sufficient Conditions ◽  
Zero Solution ◽  
Deviating Arguments ◽  
Multiple Deviating Arguments ◽  
The Subject ◽  
Functional Differential

AbstractA vector functional differential equation of the fourth order with multiple deviating arguments is considered. New sufficient conditions are established to guarantee the instability of the zero solution of the equation to be considered. We give an example to illustrate the subject.

scholarly journals Instability of a Fifth-Order Nonlinear Vector Delay Differential Equation with Multiple Deviating Arguments

2013 ◽  
Vol 2013 ◽  
pp. 1-5
Author(s):  
Cemil Tunç
Keyword(s):  
Differential Equation ◽  
Delay Differential Equation ◽  
Zero Solution ◽  
Functional Approach ◽  
Previous Literature ◽  
Deviating Arguments ◽  
Multiple Deviating Arguments ◽  
Nonlinear Vector ◽  
Delay Differential ◽  
Fifth Order

We study a fifth-order nonlinear vector delay differential equation with multiple deviating arguments. Some criteria for guaranteeing the instability of zero solution of the equation are given by using the Lyapunov-Krasovskii functional approach. Comparing with the previous literature, our result is new and complements some known results.

scholarly journals Periodicity, Stability, and Boundedness of Solutions to Certain Second Order Delay Differential Equations

2016 ◽  
Vol 2016 ◽  
pp. 1-10 ◽  
Author(s):  
A. T. Ademola ◽  
B. S. Ogundare ◽  
M. O. Ogundiran ◽  
O. A. Adesina
Keyword(s):  
Differential Equations ◽  
Delay Differential Equations ◽  
Lyapunov Functional ◽  
Second Order ◽  
Asymptotically Stable ◽  
Boundedness Of Solutions ◽  
Deviating Arguments ◽  
Nonlinear Delay Differential Equations ◽  
Delay Differential ◽  
Nonlinear Delay

The behaviour of solutions to certain second order nonlinear delay differential equations with variable deviating arguments is discussed. The main procedure lies in the properties of a complete Lyapunov functional which is used to obtain suitable criteria to guarantee existence of unique solutions that are periodic, uniformly asymptotically stable, and uniformly ultimately bounded. Obtained results are new and also complement related ones that have appeared in the literature. Moreover, examples are given to illustrate the feasibility and correctness of the main results.

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