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Title: Oscillation of deviating differential equations (English)
Author: Chatzarakis, George E.
Language: English
Journal: Mathematica Bohemica
ISSN: 0862-7959 (print)
ISSN: 2464-7136 (online)
Volume: 145
Issue: 4
Year: 2020
Pages: 435-448
Summary lang: English
Category: math
Summary: Consider the first-order linear delay (advanced) differential equation$$ x'(t)+p(t)x( \tau (t)) =0\quad (x'(t)-q(t)x(\sigma (t)) =0),\quad t\geq t_{0}, $$ where $p$ $(q)$ is a continuous function of nonnegative real numbers and the argument $\tau (t)$ $(\sigma (t))$ is not necessarily monotone. Based on an iterative technique, a new oscillation criterion is established when the well-known conditions$$ \limsup \limits _{t\rightarrow \infty }\int _{\tau (t)}^{t}p(s) {\rm d}s>1\quad \biggl (\limsup \limits _{t\rightarrow \infty }\int _{t}^{\sigma (t)}q(s) {\rm d}s>1\bigg ) $$ and $$ \liminf _{t\rightarrow \infty }\int _{\tau (t)}^{t}p(s) {\rm d}s>\frac {1}{\rm e}\quad \biggl (\liminf _{t\rightarrow \infty }\int _{t}^{\sigma (t)}q(s) {\rm d}s>\frac {1}{\rm e}\bigg ) $$ are not satisfied. An example, numerically solved in MATLAB, is also given to illustrate the applicability and strength of the obtained condition over known ones. (English)
Keyword: differential equation
Keyword: non-monotone argument
Keyword: oscillatory solution
Keyword: nonoscillatory solution
Keyword: Grönwall inequality
MSC: 34K06
MSC: 34K11
idZBL: 07286023
idMR: MR4221844
DOI: 10.21136/MB.2020.0002-19
Date available: 2020-11-18T09:58:36Z
Last updated: 2021-04-19
Stable URL:
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