Bourgin-Yang type theorem and its application to 𝑍₂-equivariant Hamiltonian systems

Izydorek, Marek

doi:10.1090/S0002-9947-99-02144-3

Bourgin-Yang type theorem and its application to $Z_2$-equivariant Hamiltonian systems
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Trans. Amer. Math. Soc. 351 (1999), 2807-2831 Request permission

Abstract:

We will be concerned with the existence of multiple periodic solutions of asymptotically linear Hamiltonian systems with the presence of $Z_2$–action. To that purpose we prove a new version of the Bourgin–Yang theorem. Using the notion of the crossing number we also introduce a new definition of the Morse index for indefinite functionals.

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