Necessary and sufficient conditions for the oscillation of delay differential equations with a piecewise constant argument
Summary: The characteristic equation for an equation with continuous and piecewise constant argument in the form \[ \dot x(t)+ px(t-\tau)+ qx([t- k])= 0,\quad\text{where }p, q\in\mathbb{R},\;\tau\in\mathbb{R}^+\text{ and }k\in \mathbb{N} \] is presented, which for \(q= 0\) reduces to \[ f(\lambda)= \lambda+ e^{-\lambda r}= 0 \] and for \(p= 0\) reduces to \[ \lambda- 1+ q\lambda^{-k}= 0. \] Necessary and sufficient conditions for oscillation are obtained.
scientific article; zbMATH DE number 1180640