Periodic solutions of delay-differential equations with a restorative condition (Q5945997)

Here, the author considers the following scalar delay equation NEWLINE\[NEWLINE x'(t)=h(x(t),x(t-\tau)),\;\tau>0.\tag{1}NEWLINE\]NEWLINE He points out, that in some applications the former equation can not be transformed into NEWLINE\[NEWLINE x'(t)=-\alpha x(t)+f(x(t-\tau)).\tag{2}NEWLINE\]NEWLINE For instance, in the model for the pupil light reflex.NEWLINENEWLINENEWLINEUnder certain condition on \(h\), the existence of periodic solutions is proved. The result is applied to concrete models.