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Subharmonics for not uniformly coercive Hamiltonian systems. (English) Zbl 1105.37035

Summary: We prove the existence of subharmonic solutions with prescribed minimal period for the Hamiltonian system \(\dot u(t)=J\nabla H(t,u(t))\) when the Hamiltonian \(H\) is subquadratic with unbounded gradient and not uniformly coercive.

MSC:

37J45 Periodic, homoclinic and heteroclinic orbits; variational methods, degree-theoretic methods (MSC2010)
34C25 Periodic solutions to ordinary differential equations
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