Abstract
We consider a class of second order Hamiltonian systems with a C^{2} potential function. The existence of new periodic solutions with a prescribed energy is established by the use of constrained variational methods.
Highlights
1 Introduction In this paper, we examine the existence of periodic solutions for second order Hamiltonian systems q + V (q) =, ( . )
Proof This follows from Sobolev’s embedding theorem and V ∈ C (Rn, R)
Summary
If the potential well x ∈ Rn : V (x) ≤ h is bounded and non-empty, the system ) has a periodic solution with energy h. ) has a non-constant periodic solution with energy h. For the weakly attractive potential V defined on an open subset of Rn, Ambrosetti and Coti Zelati [ ] ) (referred to as (Ph)) has at least one non-constant weak periodic solution with the given energy h.
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