EXISTENCE OF PERIODIC SOLUTIONS FOR HAMILTONIAN SYSTEMS WITH SUPER-LINEAR AND SIGN-CHANGING NONLINEARITIES

Liqian Jia; Guanwei Chen

doi:10.11948/2018.1524

2018 Volume 8 Issue 5

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Liqian Jia, Guanwei Chen. EXISTENCE OF PERIODIC SOLUTIONS FOR HAMILTONIAN SYSTEMS WITH SUPER-LINEAR AND SIGN-CHANGING NONLINEARITIES[J]. Journal of Applied Analysis & Computation, 2018, 8(5): 1524-1534. doi: 10.11948/2018.1524

Citation:

Liqian Jia, Guanwei Chen. EXISTENCE OF PERIODIC SOLUTIONS FOR HAMILTONIAN SYSTEMS WITH SUPER-LINEAR AND SIGN-CHANGING NONLINEARITIES[J]. Journal of Applied Analysis & Computation, 2018, 8(5): 1524-1534. doi: 10.11948/2018.1524

EXISTENCE OF PERIODIC SOLUTIONS FOR HAMILTONIAN SYSTEMS WITH SUPER-LINEAR AND SIGN-CHANGING NONLINEARITIES

School of Mathematical Sciences, University of Jinan, Jinan 250022, China

Fund Project:

Abstract

Abstract

In this paper, we consider the existence of periodic solutions for the super quadratic second order Hamiltonian system, and primitive functions of nonlinearities are allowed to be sign-changing. By using some weaker conditions, our result extends and improves some existed results in the literature.
- Second order Hamiltonian system /
- sign-changing /
- super quadratic /
- periodic solutions
MSC: 34C25;37K05;58E05

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References

[1]	F. Antonacci, Existence of periodic solutions of Hamiltonian systems with potential indefinite in sign, Nonlinear Anal., 1997, 29(12), 1353-1364. Google Scholar
[2]	G. Chen and S. Ma, Periodic solutions for Hamiltonian systems without Ambrosetti-Rabinowitz condition and spectrum 0, J. Math. Anal. Appl., 2011, 379(2), 842-851. Google Scholar
[3]	G. Chen and S. Ma, Ground state periodic solutions of second order Hamiltonian systems without spectrum 0, Isr. J. Math., 2013, 198(1), 111-127. Google Scholar
[4]	I. Ekeland, Convexity Methods In Hamiltonian Mechanics, Springer Berlin, 1990. Google Scholar
[5]	G. Fei, On periodic solutions of superquadratic Hamiltonian systems, Electron. J. Differ. Eq., 2002, 2002(08), 1-12. Google Scholar
[6]	H. Gu and T. An, Existence of infinitely many periodic solutions for secondorder Hamiltonian systems, Electron. J. Differ. Eq., 2013, 2013(251), 1-10. Google Scholar
[7]	X. M. He and X. Wu, Periodic solutions for a class of nonautonomous second order Hamiltonian systems, J. Math. Anal. Appl., 2013, 341(2), 1354-1364. Google Scholar
[8]	Q. Jiang and C. L. Tang, Periodic and subharmonic solutions of a class of subquadratic second-order Hamiltonian systems, J. Math. Anal. Appl., 2007, 328(1), 380-389. Google Scholar
[9]	Y. M. Long, Multiple solutions of perturbed superquadratic second order Hamiltonian systems, Trans. Amer. Math. Soc., 1989, 311(2), 749-780. Google Scholar
[10]	C. Li, R. P. Agarwal and D. Paşca, Infinitely many periodic solutions for a class of new superquadratic second-order Hamiltonian systems, Appl. Math. Lett., 2017, 64, 113-118. Google Scholar
[11]	C. Li, Z. Q. Ou and D. L. Wu, On the existence of minimal periodic solutions for a class of second-order Hamiltonian systems, Appl. Math. Lett., 2015, 43, 44-48. Google Scholar
[12]	L. Li and M. Schechter, Existence solutions for second order Hamiltonian systems, Nonlinear Anal-Real., 2016, 27, 283-296. Google Scholar
[13]	S. J. Li and M. Willem, Applications of local linking to critical point theory, J. Math. Anal. Appl., 1995, 189(1), 6-32. Google Scholar
[14]	J. Mawhin and M. Willem, Critical point theory and Hamiltonian systems, Springer-Verlag, 1989, 74(2), 339-359. Google Scholar
[15]	F. Meng and J. Yang, Periodic solutions for a class of non-autonomous second order systems, Int. J. Nonlin. Sci., 2010, 10(3), 342-348. Google Scholar
[16]	J. Pipan and M. Schechter, Non-autonomous second order Hamiltonian systems, J. Differ. Equations, 2014, 257(2), 351-373. Google Scholar
[17]	P. H. Rabinowitz, Periodic solutions of Hamiltonian systems, Comm. Pure Appl. Math., 1978, 31, 157-184. Google Scholar
[18]	P. H. Rabinowitz, Multiple critical points of perturbed symmetric functionals, Trans. Amer. Math. Soc., 1982, 272(2), 753-769. Google Scholar
[19]	M. Schechter, Ground state solutions for non-autonomous dynamical systems, J. Math. Phys., 2014, 55(10), 367-379. Google Scholar
[20]	M. Schechter, Periodic second order superlinear Hamiltonian systems, J. Math. Anal. Appl., 2015, 426(1), 546-562. Google Scholar
[21]	X. H. Tang and J. Jiang, Existence and multiplicity of periodic solutions for a class of second-order Hamiltonian systems, Comput. Math. Appl., 2010, 59(12), 3646-3655. Google Scholar
[22]	Z. L. Tao and C. L. Tang, Periodic and subharmonic solutions of second-order Hamiltonian systems, J. Math. Anal. Appl., 2004, 293(2), 435-445. Google Scholar
[23]	C. L. Tang and X. P. Wu, Periodic solutions for a class of new superquadratic second order Hamiltonian systems, Appl. Math. Lett., 2014, 34(2), 65-71. Google Scholar
[24]	Z. L. Tao, S. Yan and S. L. Wu, Periodic solutions for a class of superquadratic Hamiltonian systems, J. Math. Anal. Appl., 2007, 331(1), 152-158. Google Scholar
[25]	Z. Wang and J. Xiao, On periodic solutions of subquadratic second order nonautonomous Hamiltonian systems, Appl. Math. Lett., 2015, 40(72), 72-77. Google Scholar
[26]	Z. Wang and J. Zhang, New existence results on periodic solutions of nonautonomous second order Hamiltonian systems, Appl. Math. Lett., 2018, 79, 43-50. Google Scholar
[27]	Z. Wang, J. Zhang and Z. Zhang, Periodic solutions of second order nonautonomous Hamiltonian systems with local superquadratic potential, Nonlinear Anal., 2009, 70(10), 3672-3681. Google Scholar
[28]	M. H. Yang, Y. F. Chen and Y. F. Xue, Infinitely many periodic solutions for a class of scond-order Hamiltonian systems, Acta. Math. Appl. Sin-E., 2016, 32(1), 231-238. Google Scholar
[29]	Q. Yin and D. Liu, Periodic solutions of a class of superquadratic second order Hamiltonian systems, Appl. Math. J. Chinese Univ. Ser. B., 2000, 15(3), 259-266. Google Scholar
[30]	Y. Ye and C. L. Tang, Periodic and subharmonic solutions for a class of superquadratic second order Hamiltonian systems, Nonlinear Anal., 2009, 71(5-6), 2298-2307. Google Scholar
[31]	Y. Ye and C. L. Tang, Periodic solutions for second order Hamiltonian systems with general superquadratic potential, B. Belg. Math. Soc-Sim., 2014, 19(1), 747-761. Google Scholar
[32]	F. Zhao, J. Chen and M. Yang, A periodic solution for a second-order asymptotically linear Hamiltonian system, Nonlinear Anal., 2009, 70(11), 4021-4026. Google Scholar
[33]	W. Zou and S. Li, Infinitely many solutions for Hamiltonian systems, J. Differ. Equations, 2002, 186(1), 141-164. Google Scholar
[34]	Q. Zhang and C. Liu, Infinitely many periodic solutions for second-order Hamiltonian systems, J. Differ. Equations, 2011, 251(4), 816-833. Google Scholar
[35]	Q. Zhang and X. H. Tang, New existence of periodic solutions for second order non-autonomous Hamiltonian systems, J. Math. Anal. Appl., 2010, 369(1), 357-367. Google Scholar