Frontiers of Mathematics in China >

2018 , Vol. 13 >Issue 5: 1063 - 1073

DOI: https://doi.org/10.1007/s11464-018-0721-0

RESEARCH ARTICLE

Minimal periodic solutions of first-order convex Hamiltonian systems with anisotropic growth

  • Chungen LIU , 1 ,
  • Li ZUO 2 ,
  • Xiaofei ZHANG 2
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  • 1. School of Mathematics and Information Science, Guangzhou University, Guangzhou 510006, China
  • 2. School of Mathematics, Nankai University, Tianjin 300071, China

Received date: 21 May 2018

Accepted date: 04 Aug 2018

Published date: 29 Oct 2018

Copyright

2018 Higher Education Press and Springer-Verlag GmbH Germany, part of Springer Nature
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Cite this article

Chungen LIU , Li ZUO , Xiaofei ZHANG . Minimal periodic solutions of first-order convex Hamiltonian systems with anisotropic growth[J]. Frontiers of Mathematics in China, 2018 , 13(5) : 1063 -1073 . DOI: 10.1007/s11464-018-0721-0

References

Publishing order | Descend order by publishing year | Descend order by cited within
1
An T, Wang Z. Periodic solutions of Hamiltonian systems with anisotropic growth. Commun Pure Appl Anal, 2010, 9: 1069–1082

DOI

2
Aubin J-P. Mathematical Methods of Game and Economic Theory. Amsterdam: North-Holland, 1979

3
Clarke F H, Ekeland I. Hamiltonian trajectories having prescribed minimal period. Comm Pure Appl Math, 1980, 33: 103–116

DOI

4
Dong D, Long Y. The iteration formula of the Maslov-type index theory with applications to nonlinear Hamiltonian systems. Trans Amer Math Soc, 1997, 349: 2619–2661

DOI

5
Ekeland I. Convexity Methods in Hamiltonian Mechanics. Berlin: Springer, 1990

DOI

6
Ekeland I, Hofer H. Periodic solutions with prescribed minimal period for convex autonomous Hamiltonian systems. Invent Math, 1985, 81: 155–188

DOI

7
Fei G, Kim S, Wang T. Minimal period estimates of period solutions for superquadratic Hamiltonian systems. J Math Anal Appl, 1999, 238: 216–233

DOI

8
Fei G, Qiu Q. Minimal period solutions of nonlinear Hamiltonian systems. Nonlinear Anal, 1996, 27: 821–839

DOI

9
Felmer P L. Periodic solutions of “superquadratic” Hamiltonian systems. J Differential Equations, 1993, 18: 188–207

DOI

10
Li C. The study of minimal period estimates for brake orbits of autonomous subquadratic Hamiltonian systems. Acta Math Sin (Engl Ser), 2015, 31: 1645–1658

DOI

11
Liu C. Minimal period estimates for brake orbits of nonlinear symmetric Hamiltonian systems. Discrete Contin Dyn Syst, 2010, 27: 337–355

DOI

12
Liu C, Zhang X. Subharmonic solutions and minimal periodic solutions of first-order Hamiltonian systems with anisotropic growth. Discrete Contin Dyn Syst, 2017, 37: 1559–1574

13
Long Y. The minimal period problem for classical Hamiltonian systems with even potentials. Ann Inst H Poincaré Anal Non Linéaire, 1993, 10: 605–626

DOI

14
Long Y. The minimal period problem of periodic solutions for autonomous superquadratic second order Hamiltonian systems. J Differential Equations, 1994, 111: 147–174

DOI

15
Long Y. On the minimal period for periodic solutions of nonlinear Hamiltonian systems. Chin Ann Math Ser B, 1997, 18: 481–485

16
Mawhin J, Willem M. Critical Point Theory and Hamiltonian Systems. Berlin: Springer, 1989

DOI

17
Rabinowitz P H. Periodic solutions of Hamiltonian systems. Comm Pure Appl Math, 1978, 31: 157–184

DOI

18
Rabinowitz P H. Periodic solutions of Hamiltonian systems: a survey. SIAM J Math Anal, 1982, 13: 343–352

DOI

19
Roberts A, Varberg D. Another proof that convex functions are locally Lipschitz. Amer Math Monthly, 1974, 81: 1014–1016

DOI

20
Xing Q, Guo F, Zhang X. One generalized critical point theorem and its applications on super-quadratic Hamiltonian systems. Taiwanese J Math, 2016, 20: 1093–1116

DOI

21
Zhang D. Symmetric period solutions with prescribed minimal period for even autonomous semipositive Hamiltonian systems. Sci China Math, 2014, 57: 81–96

DOI

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