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Minimal period estimates on P-symmetric periodic solutions of first-order mild superquadratic Hamiltonian systems |
Xiaofei ZHANG1, Chungen LIU2() |
1. School of Mathematics and Statistics, Shanxi Datong University, Datong 037009, China 2. School of Mathematics and Information Science, Guangzhou University, Guangzhou 510006, China |
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Abstract With the aid of P-index iteration theory, we consider the minimal period estimates on P-symmetric periodic solutions of nonlinear P-symmetric Hamiltonian systems with mild superquadratic growth.
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Keywords
Hamiltonian system
P-symmetric periodic solution
P-index
minimal period
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Corresponding Author(s):
Chungen LIU
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Issue Date: 26 March 2021
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1 |
A Abbondandolo. Index estimates for strongly indefinite functionals, periodic orbits and homoclinic solutions of first order Hamiltonian systems. Calc Var Partial Differential Equations, 2000, 11: 395–430
https://doi.org/10.1007/s005260000046
|
2 |
A Abbondandolo. Morse Theory for Hamiltonian Systems. Chapman & Hall/CRC Res Notes in Math, Vol 425. London: Chapman & Hall/CRC, 2001
https://doi.org/10.1201/9781482285741
|
3 |
A Chenciner, R Montgomery. A remarkable periodic solution of the three body problem in the case of equal masses. Ann of Math, 2000, 152: 881–901
https://doi.org/10.2307/2661357
|
4 |
D Dong, Y M Long. The iteration formula of the Maslov-type index theory with applications to nonlinear Hamiltonian systems. Trans Amer Math Soc, 1997, 349: 2619–2661
https://doi.org/10.1090/S0002-9947-97-01718-2
|
5 |
Y J Dong. P-index theory for linear Hamiltonian systems and multiple solutions for nonlinear Hamiltonian systems. Nonlinearity, 2006, 19: 1275–1294
https://doi.org/10.1088/0951-7715/19/6/004
|
6 |
I Ekeland, H Hofer. Periodic solutions with prescribed minimal period for convex autonomous Hamiltonian systems. Invent Math, 1985, 81: 155–188
https://doi.org/10.1007/BF01388776
|
7 |
X J Hu, S Z Sun. Index and stability of symmetric periodic orbits in Hamiltonian systems with application to figure-eight orbit. Comm Math Phys, 2009, 290: 737–777
https://doi.org/10.1007/s00220-009-0860-y
|
8 |
X J Hu, S Z Sun. Stability of relative equilibria and Morse index of central configurations. C R Acad Sci Paris, Ser I, 2009, 347: 1309–1312
https://doi.org/10.1016/j.crma.2009.09.023
|
9 |
X J Hu, S Z Sun. Morse index and the stability of closed geodesics. Sci China Math, 2010, 53: 1207–1212
https://doi.org/10.1007/s11425-010-0064-0
|
10 |
C G Liu. Maslov P-index theory for a symplectic path with applications. Chin Ann Math Ser B, 2006, 27(4): 441–458
https://doi.org/10.1007/s11401-004-0365-0
|
11 |
C G Liu. Periodic solutions of asymptotically linear delay differential systems via Hamiltonian systems. J Differential Equations, 2012, 252: 5712–5734
https://doi.org/10.1016/j.jde.2012.02.009
|
12 |
C G Liu. Relative index theories and applications. Topol Methods Nonlinear Anal, 2017, 49: 587–614
|
13 |
C G Liu. Index Theory in Nonlinear Analysis.Berlin/Beijing: Springer/Science Press, 2019
|
14 |
C G Liu, Y M Long. Iteration inequalities of the Maslov-type index theory with applications. J Differential Equations, 2000, 165: 355–376
https://doi.org/10.1006/jdeq.2000.3775
|
15 |
C G Liu, S S Tang. Maslov (P, ω)-index theory for symplectic paths. Adv Nonlinear Stud, 2015, 15: 963–990
https://doi.org/10.1515/ans-2015-0412
|
16 |
C G Liu, S S Tang. Iteration inequalities of the Maslov P-index theory with applications. Nonlinear Anal, 2015, 127: 215–234
|
17 |
C G Liu, S S Tang. Subharmonic Pl-solutions of first order Hamiltonian systems. J Math Anal Appl, 2017, 453: 338–359
https://doi.org/10.1016/j.jmaa.2017.03.046
|
18 |
C G Liu, B X Zhou. Minimal P-symmetric period problem of first-order autonomous Hamiltonian systems. Front Math China, 2017, 12(3): 641–654
https://doi.org/10.1007/s11464-017-0627-2
|
19 |
Y M Long. Index Theory for Symplectic Paths with Applications. Progr Math, Vol 207. Basel: Birkhauser Verlag, 2002
https://doi.org/10.1007/978-3-0348-8175-3
|
20 |
P H Rabinowitz. Periodic solutions of Hamiltonian systems. Comm Pure Appl Math, 1978, 31: 157–184
https://doi.org/10.1002/cpa.3160310203
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