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Periodic solutions for nonsmooth second‐order Hamiltonian systems
Author(s) -
Deng Yiyang,
Li Fengying,
Li Bingyu,
lv Ying
Publication year - 2018
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.5308
Subject(s) - mathematics , lipschitz continuity , hamiltonian system , saddle point , hamiltonian (control theory) , smoothness , order (exchange) , pure mathematics , mathematical analysis , mathematical optimization , geometry , finance , economics
We apply the saddle–point‐type theorems of Rabinowitz and Benci‐Rabinowitz for local Lipschitz functionals that entails an extension of the classical Palais‐Smale‐Cerami condition for a C 1 functional to this setting to show the existence of new periodic solutions for second‐order Hamiltonian systems with local Lipschitz potentials, which are weaker than Rabinowitz's original conditions. The key difficulty in these arguments arises from the lack of smoothness and symmetry in the potential when extending the Cerami‐Palais‐Smale condition for the local Lipschitz case.