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In this paper we prove a lower bound for the least number of one-periodicsolutions of nondegenerate locally Hamiltonian equations on compact symplecticmanifolds in terms of the Betti numbers of the Novikov homology associated tothe Calabi invariant of the locally Hamiltonian equations. Our result improveslower bounds obtained by L\^e-Ono and Ono for the least number of nondegeneratelocally Hamiltonian symplectic fixed points. Our result also generalizes thehomological Arnold conjecture proved by Fukaya-Ono and Liu-Tian.

The Calabi invariant and the least number of periodic solutions of locally Hamiltonian equations