Hartman and Nirenberg type results for systems of delay differential equations under $ (\omega,Q) $-periodic conditions

We consider the \begin{document}$ (\omega,Q) $\end{document} -periodic problem for a system of delay differential equations, where \begin{document}$ Q $\end{document} is an invertible matrix. Existence and multiplicity of solutions is proven under different conditions that extend well-known results for the periodic case \begin{document}$ Q = I $\end{document} and anti-periodic case \begin{document}$ Q = -I $\end{document} . In particular, the results apply to biological models with mixed terms of Nicholson, Lasota or Mackey type, and also vectorial versions of Nicholson or Mackey-Glass models.

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