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# Article

 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 . 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