An iterative scheme for the oscillation criteria of a nonlinear delay differential equation with several deviating arguments

Iterative Process ◽

Iterative Scheme ◽

Deviating Arguments ◽

First Order ◽

Delay Differential ◽

This paper deals with the oscillatory results of first order nonlinear delay differential equations with several deviating arguments by employing an iterative process. The results presented here has improved the outcomes of [1, 2, 8]. Various examples are solved in MATLAB software to illustrate the relevance of the main results.

Bifurcating periodic solution for a class of first-order nonlinear delay differential equation after Hopf bifurcation

Applied Mathematical Modelling ◽

10.1016/j.apm.2011.12.020 ◽

2012 ◽

Vol 36 (10) ◽

pp. 4837-4846 ◽

Cited By ~ 1

Author(s):

Zhongjin Guo ◽

A.Y.T. Leung ◽

Y.C. Liu ◽

H.X. Yang

Keyword(s):

Differential Equation ◽

Periodic Solution ◽

Hopf Bifurcation ◽

Delay Differential Equation ◽

First Order ◽

Delay Differential ◽

Bifurcating Periodic Solution ◽

A Legendre–Gauss–Radau spectral collocation method for first order nonlinear delay differential equations

CALCOLO ◽

10.1007/s10092-015-0169-5 ◽

2015 ◽

Vol 53 (4) ◽

pp. 691-721 ◽

Cited By ~ 8

Author(s):

Lijun Yi ◽

Zhongqing Wang

Keyword(s):

Differential Equations ◽

Collocation Method ◽

Spectral Collocation Method ◽

Spectral Collocation ◽

First Order ◽

Delay Differential ◽

OSCILLATION ANALYSIS OF NUMERICAL SOLUTIONS FOR NONLINEAR DELAY DIFFERENTIAL EQUATIONS OF POPULATION DYNAMICS

Mathematical Modelling and Analysis ◽

10.3846/13926292.2011.601768 ◽

2011 ◽

Vol 16 (3) ◽

pp. 365-375 ◽

Cited By ~ 9

Author(s):

Jianfang Gao ◽

Minghui Song ◽

Mingzhu Liu

Keyword(s):

Population Dynamics ◽

Numerical Experiments ◽

Numerical Solutions ◽

Lung Ventilation ◽

Oscillation Analysis ◽

Delay Differential ◽

This paper is concerned with oscillations of numerical solutions for the nonlinear delay differential equation of population dynamics. The equation proposed by Mackey and Glass for a ”dynamic disease” involves respiratory disorders and its solution resembles the envelope of lung ventilation for pathological breathing, called Cheyne-Stokes respiration. Some conditions under which the numerical solution is oscillatory are obtained. The properties of non-oscillatory numerical solutions are investigated. To verify our results, we give numerical experiments.

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

Abstract and Applied Analysis ◽

10.1155/2009/484158 ◽

2009 ◽

Vol 2009 ◽

pp. 1-7 ◽

Cited By ~ 6

Author(s):

Chengmin Hou ◽

Sui Sun Cheng

Keyword(s):

Differential Equations ◽

Fourth Order ◽

Third Order ◽

All Solutions ◽

Linear Differential ◽

Delay Differential ◽

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.

Oscillatory and monotone solutions of first-order nonlinear delay differential equations

Georgian Mathematical Journal ◽

10.1515/gmj-2016-0015 ◽

2016 ◽

Vol 23 (2) ◽

Author(s):

Nino Partsvania ◽

Zaza Sokhadze

Keyword(s):

Differential Equations ◽

Sufficient Conditions ◽

First Order ◽

Kneser Solution ◽

Delay Differential ◽

Necessary And Sufficient ◽

Monotone Solutions ◽

AbstractFor first order nonlinear delay differential equations, necessary and sufficient conditions are established for the oscillation of all proper solutions as well as for the existence of at least one vanishing at infinity proper Kneser solution.

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

International Journal of Differential Equations ◽

10.1155/2016/2843709 ◽

2016 ◽

Vol 2016 ◽

pp. 1-10 ◽

Cited By ~ 1

Author(s):

A. T. Ademola ◽

B. S. Ogundare ◽

M. O. Ogundiran ◽

O. A. Adesina

Keyword(s):

Differential Equations ◽

Lyapunov Functional ◽

Second Order ◽

Asymptotically Stable ◽

Boundedness Of Solutions ◽

Deviating Arguments ◽

Delay Differential ◽

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.