MINIMAL PERIOD SYMMETRIC SOLUTIONS FOR SOME HAMILTONIAN SYSTEMS VIA THE NEHARI MANIFOLD METHOD

doi:10.1007/s10473-020-0302-7

数学物理学报(英文版) ›› 2020, Vol. 40 ›› Issue (3): 614-624.doi: 10.1007/s10473-020-0302-7

MINIMAL PERIOD SYMMETRIC SOLUTIONS FOR SOME HAMILTONIAN SYSTEMS VIA THE NEHARI MANIFOLD METHOD

Chouha?d SOUISSI

Department of Mathematics, Faculty of Sciences of Monastir, University of Monastir, 5000-Monastir, Tunisia

收稿日期:2018-02-06 修回日期:2018-04-21 出版日期:2020-06-25 发布日期:2020-07-17
作者简介:Chouhaïd SOUISSI,E-mail:chsouissi@yahoo.fr

MINIMAL PERIOD SYMMETRIC SOLUTIONS FOR SOME HAMILTONIAN SYSTEMS VIA THE NEHARI MANIFOLD METHOD

Chouha?d SOUISSI

Department of Mathematics, Faculty of Sciences of Monastir, University of Monastir, 5000-Monastir, Tunisia

Received:2018-02-06 Revised:2018-04-21 Online:2020-06-25 Published:2020-07-17

摘要/Abstract

摘要： For a given T > 0, we prove, under the global ARS-condition and using the Nehari manifold method, the existence of a T-periodic solution having the W-symmetry introduced in[21], for the hamiltonian system
z+ V'(z)=0, z ∈ R^N, N ∈ N^*.
Moreover, such a solution is shown to have T as a minimal period without relaying to any index theory. A multiplicity result is also proved under the same condition.

关键词: Hamiltonian, variational, minimal period, Nehari Manifold

Abstract: For a given T > 0, we prove, under the global ARS-condition and using the Nehari manifold method, the existence of a T-periodic solution having the W-symmetry introduced in[21], for the hamiltonian system
z+ V'(z)=0, z ∈ R^N, N ∈ N^*.
Moreover, such a solution is shown to have T as a minimal period without relaying to any index theory. A multiplicity result is also proved under the same condition.

Key words: Hamiltonian, variational, minimal period, Nehari Manifold

中图分类号:

35J15

Chouha?d SOUISSI. MINIMAL PERIOD SYMMETRIC SOLUTIONS FOR SOME HAMILTONIAN SYSTEMS VIA THE NEHARI MANIFOLD METHOD[J]. 数学物理学报(英文版), 2020, 40(3): 614-624.

Chouha?d SOUISSI. MINIMAL PERIOD SYMMETRIC SOLUTIONS FOR SOME HAMILTONIAN SYSTEMS VIA THE NEHARI MANIFOLD METHOD[J]. Acta mathematica scientia,Series B, 2020, 40(3): 614-624.

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MINIMAL PERIOD SYMMETRIC SOLUTIONS FOR SOME HAMILTONIAN SYSTEMS VIA THE NEHARI MANIFOLD METHOD

MINIMAL PERIOD SYMMETRIC SOLUTIONS FOR SOME HAMILTONIAN SYSTEMS VIA THE NEHARI MANIFOLD METHOD

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