Refaad for Studies, Research and Developement
An Oscillation Criterion in Delay Diﬀerential Equations
25199269 (Print)
25199277 (Online)
Volume 5
Issue 1
2018

0
An Oscillation Criterion in Delay Diﬀerential Equations
1
6
English
George E. ChatzarakisDepartment of Electrical and Electronic Engineering Educators, School of Pedagogical and Technological Education (ASPETE) 14121, N. Heraklio, Athens, Greece geaxatz@otenet.gr, gea.xatz@aspete.gr
https://doi.org/10.31559/glm2018.5.1.1
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 wellknown 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.
diﬀerential equation; nonmonotone argument; oscillatory solution; nonoscillatory solution; Gr¨onwall inequality.
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http://www.refaad.com/Files/GLM/GLM511.pdf