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Infinitely many periodic solutions for second order Hamiltonian systems. (English) Zbl 1230.37081

Consider the second order Hamiltonian system

u ¨(t)+ u V(t,u(t))=0,u(0)=u(T),u ˙(0)=u ˙(T),

where t, VC 1 (× N ,) is T-periodic and it has the form V(t,u)=1 2U(t)u,u+W(t,u) with U a continuous T-periodic symmetric matrix, and ·,· the standard inner product in N . The authors study the existence of infinitely many nontrivial solutions of this system using the variant fountain theorems obtained by W. Zou [Manuscr. Math. 104, No. 3, 343–358 (2001; Zbl 0976.35026)], under the hypothesis that W(t,u) is even in the variable u.

MSC:
37J45Periodic, homoclinic and heteroclinic orbits; variational methods, degree-theoretic methods
34C25Periodic solutions of ODE
47J30Variational methods (nonlinear operator equations)
58E05Abstract critical point theory
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