An Oscillation Criterion in Delay Differential Equations

Volume 5, Issue 1, Article 1 - 2018

Authors: George E. Chatzarakis

Copyright © 2018 . This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

 Download PDF File

 Share on GOOGLE+  Share on Twitter  Share on LinkedIn Open XML File

Abstract

Consider the first order linear delay differential equation x0(t) + p(t)x(τ(t)) = 0, t ≥ t0, where p is a continuous function of nonnegative real numbers and the argument τ(t) is not necessarily monotone. Based on an iterative technique, a new oscillation criterion is established when the well-known oscillation conditions limsupt→∞ t τ(t)p(s)ds > 1 and liminft→∞ t τ(t)p(s)ds > 1 e are not satisfied. An example, numerically solved in MATLAB, is also given to illustrates the applicability and strength of the obtained condition over known ones.

How To Cite This Article

@article{E_Chatzarakis_2018, doi = {10.31559/glm2018.5.1.1}, url = {https://doi.org/10.31559%2Fglm2018.5.1.1}, year = 2018, month = {aug}, publisher = {Refaad for Studies and Research}, volume = {5}, number = {1}, pages = {1--6}, author = {George E. Chatzarakis}, title = {An Oscillation Criterion in Delay Differential Equations}, journal = {General Letters in Mathematics} }
E. Chatzarakis, G. (2018). An Oscillation Criterion in Delay Differential Equations. General Letters in Mathematics, 5(1), 1–6. doi:10.31559/glm2018.5.1.1
[1]G. E. Chatzarakis, “An Oscillation Criterion in Delay Differential Equations,” General Letters in Mathematics, vol. 5, no. 1, pp. 1–6, Aug. 2018.
E. Chatzarakis, George. “An Oscillation Criterion in Delay Differential Equations.” General Letters in Mathematics 5, no. 1 (August 2018): 1–6. doi:10.31559/glm2018.5.1.1.