Subharmonics near an equilibrium point for hamitonian systems

Felmer, Patricio

doi:10.1007/bf02568504

Cited by 4 publications

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“…More relaxed nonresonance conditions on the linearised equation are allowed by assuming the nondegeneracy condition, together with a sign assumption. See Rabinowitz [9], Benci and Fortunato [1,2] and Felmer [4]. See [1], in particular, for second-order problems.…”

Section: Introductionmentioning

confidence: 99%

Subharmonics near an equilibrium for some second-order Hamiltonian systems

Felmer

Silva

1993

Proceedings of the Royal Society of Edinburgh: Section A Mathem

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SynopsisThis work is devoted to the study of subharmonic solutions of a second-order Hamiltonian systemnear an equilibrium point, say q = 0. The problem of existence of periodic solutions from the global point of view is also considered.This problem has been studied for the case where the potential is positive and superquadratic. In this work a potential V that has change in sign is considered. The potential is decomposed aswhere P is homogeneous, superquadratic and nondegenerate, and is of higher order near 0. In this paper the existence is shown of a sequence of subharmonic solutions of the equation above that converges to the equilibrium, such that their minimal periods converge to infinity.This problem is approached from a variational point of view. Existence of subharmonic and periodic solutions is obtained via minimax techniques.

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