#### TED University Mathematics Department Seminars

Oscillations of Differential and Difference Equations with Several Deviating Arguments
Ioannis P. Stavroulakis
University of Ioannina, Greece
Özet : Consider the first-order delay differential equation \begin{equation*} x^{\prime }(t)+\sum_{i=1}^{m}p_{i}(t)x(\tau _{i}(t))=0,\quad t\geq 0, \end{equation*} where, for every $i\in \left\{ 1,\ldots ,m\right\}$, $p_{i}$ is a continuous real-valued function in the interval $[0,\infty ),$ and $\tau _{i}$ is a continuous real-valued function on $[0,\infty )$ such that \begin{equation*} \tau _{i}(t)\leq t\quad t\geq 0\quad \text{and}\quad \lim_{t\rightarrow \infty }\tau _{i}(t)=\infty \end{equation*} and the discrete analogue difference equation \begin{equation*} \Delta x(n)+\sum_{i=1}^{m}p_{i}(n)x(\tau _{i}(n))=0\quad n\in \mathbb{N}_{0} \end{equation*} where $m\in \mathbb{N}$, $p_{i}$, $1\leq i\leq m$, are real sequences and $\left\{ \tau _{i}(n)\right\} _{n\in \mathbb{N}_{0}}$, $1\leq i\leq m$, are sequences of integers such that \begin{equation*} \tau _{i}(n)\leq n-1 \quad n\in \mathbb{N}_{0}\quad \text{and}\quad\lim\limits_{n\rightarrow \infty }\tau _{i}(n)=\infty \quad 1\leq i\leq m \end{equation*} Several optimal oscillation conditions for the above equations are presented.
 Tarih : 23.03.2017 Saat : 16:00 Yer : TED Üniversitesi, A216 Dil : English Ek Dosya : Özet