Opuscula Math. 39, no. 3 (2019), 321-353
https://doi.org/10.7494/OpMath.2019.39.3.321

Opuscula Mathematica

# Oscillations of equations caused by several deviating arguments

George E. Chatzarakis

Abstract. Linear delay or advanced differential equations with variable coefficients and several not necessarily monotone arguments are considered, and some new oscillation criteria are given. More precisely, sufficient conditions, involving $$\lim\sup$$ and $$\lim\inf$$, are obtained, which essentially improve several known criteria existing in the literature. Examples illustrating the results are also given, numerically solved in MATLAB.

Keywords: differential equation, non-monotone argument, oscillatory solution, nonoscillatory solution.

Mathematics Subject Classification: 34K11, 34K06.

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• George E. Chatzarakis
• https://orcid.org/0000-0002-0477-1895
• School of Pedagogical and Technological Education (ASPETE), Department of Electrical and Electronic Engineering Educators, 14121, N. Heraklio, Athens, Greece
• Communicated by Josef Diblík.
• Accepted: 2018-12-23.
• Published online: 2019-02-23.