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二阶哈密顿系统的同宿轨

DOI: 10.3969/j.issn.1001-8395.2015.02.003, PP. 169-171

Keywords: 同宿轨,哈密顿系统,变分法,傅里叶分析

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Abstract:

利用变分法和傅里叶分析,研究了当势函数满足一定条件时的二阶哈密顿系统同宿轨的存在性.传统的方法是利用山路引理,寻找鞍点型临界点来解决同宿轨的存在性.使用了不常用的变分直接方法,推广前人的结论,证明当势函数满足较弱的条件时同宿轨的存在性.

References

[1]  Ambrosetti A, Zelati V C. Closed orbits of fixed energy for singular Hamiltonian systems[J]. Arch Rat Mech Anal,1990(112):339-362.
[2]  Ambrosetti A, Zelati V C. Closed orbits of fixed energy for a class of N-body problems[J]. Ann Inst H Poincare:Analyse Non Lineare,1992(9):187-200.
[3]  Ambrosetti A, Zelati V C. Pericodic Solutions for Singular Lagrangian Systems[M]. Berlin:Springer-Verlag,1993.
[4]  Benci V, Giannoni G. Periodic solutions of prescribed energy for a class of Hamiltonian system with singular potentials[J]. J Diff Eqns,82(1989):60-70.
[5]  Gluck H, Ziller W. Existence of periodic motions of conservative systems, in Seminar on Minimal Submanifolds[C]//Bombieri E Ed.Princeton:Princeton Univ Press,1983.
[6]  Greco C. Periodic solutions of a class of singular Hamiltonian systems[J]. Nonlinear Anal:TMA,1988,12:259-269.
[7]  Rabinowitz P H. Homoclinic orbits for a class of Hamiltonian systems[J]. Proceedings of the Royal Society of Edinburgh,1990,A114:33-38.
[8]  Rabinowitz P H. Homoclinic and heteroclinic orbits for a class of Hamiltonian systems[J]. Calc Var Part Diff Eqns,1993:1-36.
[9]  Ekeland I. Convexity Methods in Hamiltonian Mechanics[M]. Berlin:Springer-Verlag,1990.
[10]  Ekeland I. Variational Methods[M]. Berlin:Springer-Verlag,1990.
[11]  Adams R A, Fournier J F. Sobolev Spaces, Second Edition[M]. New York:Academic Press,2003.
[12]  Ambrosetti A, Rabinowitz P. Dual variational methods in critical point theory and applications[J]. J Funct Anal,1973,14:349-381.
[13]  Bahri A, Rabinowitz P H. A minimax method for a class of Hamiltonian systems with singular potentials[J]. J Funct Anal,1989,82:412-428.
[14]  Benci V, Rabinowitz P. Critical point theorem for indefinite functionals[J]. Invent Math,1979,52:241-273.
[15]  Benci V. Closed geodesics for the Jacobi metric and periodic solutions of prescribed energy of natural Hamiltonian systems[J]. Ann Inst Henri Poincare Anal NonLineaire,1984(1):401-412.
[16]  Carminati C, Sere K, Tanaka E. The fixed energy problem for a class of nonconvex singular hamiltonian systems[J]. J Diff Eqns,2006,230(1):362-377.
[17]  Wu D L, Wu X P, Tang C L. Homoclinic solutions for a class of non-periodic and non-even second-order Hamiltonian systems[J]. J Math Anal Appl,2010(367):154-166
[18]  Hayashi K. Periodic Solutions of Classical Hamiltonian Systems[M]. Tokyo:Tokyo J Math,1983.
[19]  Ziemer W P. Weakly differentiable functions[M]. Berlin:Springer-Verlag,1989.

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