Periodic solutions of a differential equation with a discontinuous delayed neutral-type feedback

We consider a differential equation with a discontinuous delayed neutral-type feedback. In the phase space, we describe classes of initial functions that depend on a number of parameters. We show that in a certain time, solutions return to an analogous class, possibly with other parameters. The analysis of the change in the parameters allows describing periodic solutions and their stability. We show that infinitely many of stable periodic solutions exist.