We consider the (ω, 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.
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