Periodic solutions for general nonlinear state-dependent delay logistic equations (Q869830)

The paper deals with an abstract version of the logistic equation, namely with an equation of the form \[ x'(t)=\pm\delta(x(t))\Bigl[f(t, \int_{-\gamma(t)}^{-\sigma(t)}x(t+s)\,d\mu_1(t,s)-h(t, \int_{-\omega(t)}^{-\sigma(t)}x(t+s)\,d\mu_2(t,s)-g(t,x(t-\tau(t,x(t))))\Bigr], \] in two cases: \(\delta(x(t))=1\) and \(\delta(x(t))=x(t).\) It is assumed that all functions involved are \(T\)-periodic in \(t.\) The authors, by using the coincidence degree theory, prove the existence of periodic solutions under at least the condition that the quantity in the brackets is bounded over the space of all \(T\)-periodic continuous functions \(x(t).\)