Minimal periodic problem for brake orbits of first-order Hamiltonian systems
Keywords
Hamiltonian system, brake orbit, $L_{0}$-index, minimal periodic problemAbstract
In this paper, with the aid of $L_{0}$-index iteration theory, the minimal period estimates are considered on brake orbits of nonlinear $N$-symmetric Hamiltonian systems with a mild superquadratic growth condition.References
A. Abbondandolo, Morse Theory for Hamiltonian Systems, Chapman, Hall, London, 2001.
A. Ambrosetti, V. Benci and Y. Long, A note on the existence of multiple brake orbits, Nonlinear Anal. 21 (1993), 643–649.
V. Benci and F. Giannoni, A new proof of the existence of a brake orbit, Advanced Topics in the Theory of Dynanmical Systems, Notes Rep. Math. Sci. Eng. 6 (1989), 37–49.
F. Guo and C. Liu, Multiplicity of Lagrangian orbits on symmetric star-shaped hypersurfaces, Nonlinear Anal. 69 (2008), 1425–1436.
F. Guo and C. Liu, Multiplicity of characteristics with Lagrangian boundary values on symmetric star-shaped hypersurfaces, J. Math. Anal. Appl. 353 (2009), 88–98.
C. Li and C. Liu, Brake subharmonic solutions of first order Hamiltonian systems, Sci. China Math. 53 (2010), 2719–2732.
C. Li, The study of minimal period estimates for brake orbits of autonomous subquadratic Hamiltonian systems, Acta Math. Sin. (Engl. Ser.) 31 (2015), 1645–1658.
C. Li, Brake subharmonic solutions of subquadratic Hamiltonian systems, Chin. Ann. Math. Ser. B 37 (2016), 405–418.
C. Liu, Subharmonic solutions of Hamiltonian systems, Nonlinear Anal. 42 (2000), 185–198.
C. Liu, Maslov-type index theory for symplectic paths with Lagrangian boundary conditions, Adv. Nonlinear Stud. 7 (2007), 131–161.
C. Liu, Asymptotically linear Hamiltonian systems with Lagrangian boundary conditions, Pac. J. Math. 232 (2007), 233–255.
C. Liu, Minimal period estimates for brake orbits of nonlinear symmetric Hamiltonian systems, Discrete Contin. Dyn. Syst. 27 (2010), 337–355.
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 D. Zhang, Iteration theory of L-index and multiplicity of brake orbits, J. Differential Equations 257 (2014), 1194–1245.
C. Liu and D. Zhang, Seifert conjecture in the even convex case, Comm. Pure Appl. Math. 67 (2014), 1563–1604.
Y. Long, Index Theory for Symplectic Paths with Applications, Birkhäuser, Basel, 2002.
Y. Long, D. Zhang and C. Zhu, Multiple brake orbits in bounded convex symmetric domains, Adv. Math. 203 (2006), 568–635.
P.H. Rabinowitz, Periodic solutions of Hamiltonian systmes, Comm. Pure Appl. Math. 31 (1978), 157–184.
P.H. Rabinowitz, On the existence of periodic solutions for a class of symmetric Hamiltonian systems, Nonlinear Anal. 11 (1987), 599–611.
A. Szulkin, An index theory and existence of multiple brake orbits for star-shaped Hamiltonian systems, Math. Ann. 283 (1989), 241–255.
D. Zhang, Minimal period problems for brake orbits of nonlinear autonomous reversible semipositive Hamiltonian systems, Discrete Contin. Dyn. Syst. 35 (2015), 2227–2272.
X. Zhang and C. Liu, Brake orbits of first-order convex Hamiltonian systems with particular anisotropic growth, Acta Math. Sin. (Engl. Ser.) 36 (2020), 171–178.
Published
How to Cite
Issue
Section
Stats
Number of views and downloads: 0
Number of citations: 0
