Oscillation Theory of First Order Differential Equations with Delay

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Authors

  • Yutaka Shoukaku
     Faculty of Engineering, Kanazawa University, Kanazawa 920-1192 ,JP

DOI:

https://doi.org/10.18311/jims/2019/19834

Keywords:

Oscillation, First order differential equations, Delay

Abstract

In this paper we try to improve the conditions of [4]. Consequently, we introduce that

L>e-1/e-2(k + 1/λ1) - 1/e-2

is a sufficient condition for the oscillation of all solutions of first order delay differential equation

x"²(t) + p(t)x(σ(t)) = 0

under the conditions

L < 1 and 0 < k </1/e,

where k=liminft→∞∫tσ(t) p(s)ds, L=limsupt→∞∫tσ(t)p(s)ds

and λ1is the smaller root of the equation λ=ekλ

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Published

2019-08-22

How to Cite

Shoukaku, Y. (2019). Oscillation Theory of First Order Differential Equations with Delay. The Journal of the Indian Mathematical Society, 86(3-4), 315–324. https://doi.org/10.18311/jims/2019/19834

Issue

Volume 86, Issue 3-4, July-December 2019

Section

Articles

License

Copyright (c) 2019 Yutaka Shoukaku

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

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Europe PMC
Received 2018-01-24
Accepted 2019-03-20
Published 2019-08-22

 

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