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arXiv · 1309.6213

Oscillation criteria for differential equations with several retarded arguments

Gennaro Infante·Roman Koplatadze·Ioannis P. Stavroulakis
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Abstract

Consider the first-order linear differential equation with several retarded arguments $$ x^{\prime}(t)+\sum\limits_{i=1}^{m}p_{i}(t)x(τ_{i}(t))=0,\;\;\;t\geq t_{0}, $$ where the functions $p_{i},τ_{i}\in C([t_{0,}\infty),\mathbb{R}^{+}),$ for every $i=1,2,\ldots,m,$ $τ_{i}(t)\leq t$ \ for $t\geq t_{0}$ and $% \lim_{t\rightarrow \infty}τ_{i}(t)=\infty $. The state of the art on the oscillation of all solutions to these equations are established especially in the case of non-monotone arguments. Examples illustrating the results are given.

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Gennaro Infante, Roman Koplatadze, Ioannis P. Stavroulakis. 2014-03-31. Oscillation criteria for differential equations with several retarded arguments. https://doi.org/10.1619/fesi.58.347

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