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In this paper, we consider periodic predator-prey systems of Leslie-Gower orHolling-Tanner type, assuming that the coefficients are continuous positive$\omega$-periodic functions. We prove an existence of positive$\omega$-periodic solutions by means of operator method in Banach spaces withcones. No constructive conditions are required for the coefficients, besidesthe positivity and periodicity. At the end we point out that the used approachcan be applied with minor changes for proving the existence of positive$\omega$-periodic solutions even in the case of certain delays.

Positive periodic solutions for periodic predator-prey systems of Leslie-Gower or Holling-Tanner type