An equation alternately of retarded and advanced type

Abstract:

We study a differential equation with the argument $2[(t + 1)/2]$, where $[ \cdot ]$ denotes the greatest-integer function. The argument deviation $\tau (t) = t - 2[(t + 1)/2]$ is a function of period 2 and equals $t$ for $- 1 \leqslant t < 1$. It changes its sign in each interval $2n - 1 \leqslant t < 2n + 1$.