Geodesic
Periodic solutions for a class of second-order Hamiltonian systems
Electronic journal of differential equations, Tome 2005 (2005)
Multiplicity results for an eigenvalue second-order Hamiltonian system are investigated. Using suitable critical points arguments, the existence of an exactly determined open interval of positive eigenvalues for which the system admits at least three distinct periodic solutions is established. Moreover, when the energy functional related to the Hamiltonian system is not coercive, an existence result of two distinct periodic solutions is given.
Classification : 34B15, 34C25
Keywords: second order Hamiltonian systems, eigenvalue problem, periodic solutions, critical points, multiple solutions 
@article{EJDE_2005__2005__a115,
     author = {Bonanno,  Gabriele and Livrea,  Roberto},
     title = {Periodic solutions for a class of second-order {Hamiltonian} systems},
     journal = {Electronic journal of differential equations},
     year = {2005},
     volume = {2005},
     zbl = {1096.34027},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2005__2005__a115/}
}
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Bonanno,  Gabriele; Livrea,  Roberto. Periodic solutions for a class of second-order Hamiltonian systems. Electronic journal of differential equations, Tome 2005 (2005). http://geodesic.mathdoc.fr/item/EJDE_2005__2005__a115/