MINIMAL PERIOD SYMMETRIC SOLUTIONS FOR SOME HAMILTONIAN SYSTEMS VIA THE NEHARI MANIFOLD METHOD

doi:10.1007/s10473-020-0302-7

Abstract

Abstract: For a given T > 0, we prove, under the global ARS-condition and using the Nehari manifold method, the existence of a T-periodic solution having the W-symmetry introduced in[21], for the hamiltonian system
z+ V'(z)=0, z ∈ R^N, N ∈ N^*.
Moreover, such a solution is shown to have T as a minimal period without relaying to any index theory. A multiplicity result is also proved under the same condition.

Key words: Hamiltonian, variational, minimal period, Nehari Manifold

CLC Number:

35J15

Chouha?d SOUISSI. MINIMAL PERIOD SYMMETRIC SOLUTIONS FOR SOME HAMILTONIAN SYSTEMS VIA THE NEHARI MANIFOLD METHOD[J].Acta mathematica scientia,Series B, 2020, 40(3): 614-624.

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