## Characteristic multipliers and stability of symmetric periodic solutions of $$\dot x(t)=g(x(t-1))$$.(English)Zbl 0672.34069

The equation (1) $$\dot x(t)=g(x(t-1))$$ is considered where g is an odd and monotone nonlinear function. It is proved that for a certain class of such functions the nontrivial characteristic multipliers of any periodic solution of (1) satisfying $$x(t)=-x(t-2)$$, $$t\in R$$, are all strictly inside the unit circle.