Periodic solutions for differential equations with state-dependent delay and positive feedback (Q1870903)

The author explores the differential equation with state-dependent delay \[ \dot{x}(t)=\mu x(t)+f(x(t-r)),\quad r=r(x(t)), \] where \(\mu>0\), \(f\) and \(r\) are smooth real functions with \(r(0)=1\) and \(f'(0)>0\). It is proved that the delay differential equation admits a nontrivial periodic orbit and a homoclinic orbit connecting \(0\) to the periodic orbit. The paper is well written and involves some interesting techniques.