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

Abstract

We consider the (w,Q)-periodic problem for a system of delay differential equations, where Q is an invertible matrix. Existence and multiplicity of solutions is proven under different conditions that extend well-known results for the periodic case Q=I and anti-periodic case Q=-I. 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.