Oscillations and Asymptotic Stability of Entire Solutions of Linear Delay Differential Equations

Abstract

Think about the linear delay differential equation, \begin{equation}\label{1} y'(q) + \sum_{n=1}^{m} P_{n}(q) y(q-\tau_{n})=0,\quad q\geq q_{0}, \end{equation} where $P_{n}\in C([q_{0},\infty),R)$ and $\tau_{n}\geq0$ for $n=1,2,\ldots,m$. By investigating the oscillatory solutions of the linear delay differential equations, we offer new adequate condition for the asymptotic stability of the solutions of \eqref{1}. We also produce comparison result and stability of \eqref{1}.