Uniform Ultimate Boundedness of Solutions of Third-Order Nonlinear Delay Differential Equations

2010 ◽  
Vol 56 (1) ◽  
Author(s):  
Mathew Omeike
Keyword(s):  
Differential Equations ◽  
Delay Differential Equations ◽  
Boundedness Of Solutions ◽  
Ultimate Boundedness ◽  
Third Order ◽  
Uniform Ultimate Boundedness ◽  
Nonlinear Delay Differential Equations ◽  
Delay Differential ◽  
Nonlinear Delay

scholarly journals Asymptotic Dichotomy in a Class of Fourth-Order Nonlinear Delay Differential Equations with Damping

2009 ◽  
Vol 2009 ◽  
pp. 1-7 ◽  
Author(s):  
Chengmin Hou ◽  
Sui Sun Cheng
Keyword(s):  
Differential Equations ◽  
Fourth Order ◽  
Delay Differential Equations ◽  
Third Order ◽  
All Solutions ◽  
Nonlinear Delay Differential Equations ◽  
Linear Differential ◽  
Delay Differential ◽  
Nonlinear Delay Differential Equation ◽  
Nonlinear Delay

All solutions of a fourth-order nonlinear delay differential equation are shown to converge to zero or to oscillate. Novel Riccati type techniques involving third-order linear differential equations are employed. Implications in the deflection of elastic horizontal beams are also indicated.

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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