Nonexistence of periodic solutions in a class of delay-differential equations (Q2784670)

The authors investigate the nonexistence of periodic solutions to a class of integro-differential equations with distributed infinite delays where the delay kernels can be assumed to be suitably normalized convex combinations of \(\gamma\) functions. First, the authors use the so-called linear chain trick method to transform the considered system into an expanded system of ordinary differential equations. Then they apply the negative criteria established by \textit{Y. Li} and \textit{J. S. Muldowney} [J. Differ. Equations 106, No. 1, 27--39 (1993; Zbl 0786.34033)] for the existence of periodic solutions to systems of ordinary differential equations in \(\mathbb R^n\) which generalize the Bendixson and Dulac criteria to the case \(n\geq 2\). Finally, applications to a chemostat model with delays are carried out also. The present paper is a new attempt for delay differential equations and seems interesting.NEWLINENEWLINEFor the entire collection see [Zbl 0971.00016].