Subharmonic solutions and minimal periodic solutions of first-order variant subquadratic Hamiltonian systems
Słowa kluczowe
Hamiltonian system, Maslov-type index, homological link, subharmonic solution, minimal periodAbstrakt
Using the homological link theorem and iteration inequalities of Maslov-type index, we prove the multiplicity of subharmonic solutions for some variant subquadratic non-autonomous Hamiltonian systems. Moreover, the minimal period problem has also been considered for the variant subquadratic autonomous Hamiltonian systems.Bibliografia
A. Abbondandolo, Morse Theory for Hamiltonian Systems, Chapman, Hall, London, 2001.
T. An and Z. Wang, Periodic solutions of Hamiltonian systems with anisotropic growth, Commn. Pure Appl. Anal. 9 (2010), 1069–1082.
V. Benci and P.H. Rabinowitz, Critical point theorems for indefinite functionals, Inventions Math. 52 (1979), 241–273.
A. Capozzi, On subquardratic not-autonomous Hamiltonian systems, Lecture Notes in Mathematics, vol. 1017, Springer, Berlin, 1983, pp. 122–131.
A. Capozzi, On subquardratic Hamiltonian systems, Nonlinear Anal. 8 (1984), 553–562.
K. C. Chang, Infinite Dimensional Morse Theory and Multiple Solution Problems, Progress in Nonlinear Differention Equations and Their Application, vol. 6, 1993.
S. Chen and C. Tang, Periodic and subharmonic solutions of a class of superquadratic Hamiltonian systems, J. Math. Anal. Appl. 297 (2004), 267–284.
F. Clarke and I. Ekeland, Hamiltonian trajectories having prescribed minimal period, Comm. Pure Appl. Math. 33 (1980), 103–116.
D. Dong and Y. Long, The iteration formula of the Maslov-type index theory with applications to nonlinear Hamiltonian systems, Trans. Amer. Math. Soc. 349 (1997), 2619–2661.
I. Ekeland, Convexity Methods in Hamiltonian Mechanics, Springer, Berlin, 1990.
I. Ekeland and H. Hofer, Periodic solutions with prescribed minimal period for convex autonomous Hamiltonian sysmtems, Invent. Math. 81 (1985), 155–188.
I. Ekeland and H. Hofer, Subharmonics of convex nonautonomous Hamiltonian systems, Comm. Pure Appl. Math. 40 (1987), 1–37.
X. Fan and Q. Li, Periodic solutions of “subquadratic” Hamiltonian systems, Journal of LanZhou University (Natural Sciences) 32 (1996), 6–10.
G. Fei, S.K. Kim and T. Wang, Minimal period estimates of period solutions for superquadratic Hamiltonian systmes, J. Math. Anal. Appl. 238 (1999), 216–233.
G. Fei and Q. Qiu, Minimal period solutions of nonlinear Hamiltonian systems, Nonlinear Anal. 27 (1996), 821–839.
P.L. Felmer, Periodic solutions of “superquadratic” Hamiltonian systems, J. Differential Equations 102 (1993), 188–207.
F. Guo and Q. Xing, On existence of periodic solutions for one type of sub-quadratic Hamiltonian systems, Acta Sci. Natur. Univ. Nankaiensis 49 (2016), 1–8. (Chinease)
N. Hirano and Z. Wang, Subharmonic solutions for second order Hamiltonian systems, Discrete Contin. Dyn. Syst. 4 (1998), 467–474.
C. Li, Brake subharmonic solutions of subquadratic Hamiltonian systems, Chin. Ann. Math. Ser. B 37 (2016), 405–418.
C. Li and C. Liu, Brake subharmonic solutions of first order Hamiltonian systems, Science China (Mathematics) 53 (2010), 2719–2732.
C. Li, Z. Ou and C. Tang, Periodic and subharmonic solutions for a class of nonautonomous Hamiltonian systems, Nonlinear Anal. 75 (2012), 2262–2272.
C. Liu, Subharmonic solutions of Hamiltonian systems, Nonlinear Anal. 42 (2000), 185–198.
C. Liu, Minimal period estimates for brake orbits of nonlinear symmetric Hamiltonian systems, Discrete Contin. Dyn. Syst. 37 (2010), 337–355.
C. Liu, Relative index theories and applications, Topol. Methods Nonlinear Anal. 2 (2017), 587–614.
C. Liu and Y. Long, Iteration inequalities of the Maslov-type index theory with applications, J. Differential Equations 165 (2000), 355–376.
C. Liu and S. Tang, Iteration inequalities of the Maslov P -index theory with applications, Nonlinear Anal. 127 (2015), 215–234.
C. Liu and S. Tang, Subharmonic P l -solutions of first order Hamiltonian systems, J. Math. Anal. Appl. 453 (2017), 338–359.
C. Liu and X. Zhang, Subharmonic solutions and minimal periodic solutions of firstorder Hamiltonian systmes with anisotropic growth, Discrete Contin. Dyn. Syst. 37 (2017), 1559–1574.
Y. Long, Index theory for symplectic paths with application, Progress in Mathematics, vol. 207, Birkhäuser–Verlag, 2002.
R. Michalek and G. Tarantello, Subharmonic solutions with prescribed minimal period for nonautonomous Hamiltonian systems, J. Differential Equations 72 (1988), 28–55.
P.H. Rabinowitz, Periodic solutions of Hamiltonian systmes, Comm. Pure Appl. Math. 31 (1978), 157–184.
P.H. Rabinowitz, On subharmonic solutions of Hamiltonian systmes, Comm. Pure Appl. Math. 33 (1980), 609–633.
P.H. Rabinowitz, Mini-max methods in critical point theory with applications to differential equations, CBMS Reg. Conf. Ser. Math. 65, 1986.
E. Silva, Subharmonic solutions for subquadratic Hamiltonian systems, J. Differential Equations 115 (1995), 120–145.
S. Tang, Minimal P -symmetric periodic solutions of nonlinear Hamiltonian systems, (preprint).
D. Zhang, Symmetric period solutions with prescribed minimal period for even autonomous semipositive Hamiltonian systems, Sci. China Math. 57 (2014), 81–96.
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