Geodesic
Existence and Multiplicity of Periodic Solutions for Second Order Hamiltonian Systems Depending on a Parameter
Journal of convex analysis, Tome 20 (2013) no. 4, pp. 1075-1094.

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The existence of at least one nontrivial periodic solution for a class of second order Hamiltonian systems depending on a parameter is obtained, under an algebraic condition on the nonlinearity G and without requiring any asymptotic behavior neither at zero nor at infinity. The existence is still deduced in the particular case when G is subquadratic at zero. Finally, two multiplicity results are proved if G, in addition, is required to fulfill some different Ambrosetti-Rabinowitz type superquadratic conditions at infinity. The approach is fully variational.
Mots-clés : Second order Hamiltonian systems, periodic solutions, critical points 
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     author = {G. Bonanno and R. Livrea},
     title = {Existence and {Multiplicity} of {Periodic} {Solutions} for {Second} {Order} {Hamiltonian} {Systems} {Depending} on a {Parameter}},
     journal = {Journal of convex analysis},
     pages = {1075--1094},
     publisher = {mathdoc},
     volume = {20},
     number = {4},
     year = {2013},
     url = {http://geodesic.mathdoc.fr/item/JCA_2013_20_4_JCA_2013_20_4_a10/}
}
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G. Bonanno; R. Livrea. Existence and Multiplicity of Periodic Solutions for Second Order Hamiltonian Systems Depending on a Parameter. Journal of convex analysis, Tome 20 (2013) no. 4, pp. 1075-1094. http://geodesic.mathdoc.fr/item/JCA_2013_20_4_JCA_2013_20_4_a10/