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

Keywords

Hamiltonian system / minimal period / Fenchel’s transform / subdifferential

References

[1] An T, Wang Z. Periodic solutions of Hamiltonian systems with anisotropic growth. Commun Pure Appl Anal, 2010, 9: 1069–1082

[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

[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

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

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

[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

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

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

[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

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

[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

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

[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

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

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

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

[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

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

RIGHTS & PERMISSIONS

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