A sufficient condition on unbounded rotational growth guarantees T-periodic solutions for planar systems allowing finite-time blow-up, including superquadratic Hamiltonians satisfying the Ambrosetti-Rabinowitz condition.
Morris, A differential equation for undamped forced non-linear oscillations
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Existence of a periodic solution for superquadratic Hamiltonian systems with possible finite-time blow-up
A sufficient condition on unbounded rotational growth guarantees T-periodic solutions for planar systems allowing finite-time blow-up, including superquadratic Hamiltonians satisfying the Ambrosetti-Rabinowitz condition.