Infinite frequency oscillations in a class of discontinuous equations with a variable delay (Q6612571)

The paper considers the following delay differential equation \N\[\N\dot{x}(t)=-\mathrm{sign}\, x(t-\tau(t))+f(x(t)),~~t>0, \N\]\N\[\Nx(s)=\varphi(s),~-h\leq s\leq 0, \N\]\Nwhere \(\sup_{t\in R}|f(x(t))|<1\).\N\NSome sufficient conditions are obtained for distribution of zero points of the solution and the non-existence of oscillatory solutions with infinite frequency.