[1] Yin Cuicui, Zhang Fubao, Huang Chengshan,. Infinitely many periodic solutionsfor second-order Hamiltonian systems [J]. Journal of Southeast University (English Edition), 2009, 25 (4): 549-551. [doi:10.3969/j.issn.1003-7985.2009.04.028]

Copy

Infinitely many periodic solutionsfor second-order Hamiltonian systems()

Share：

Journal of Southeast University (English Edition)[ISSN:1003-7985/CN:32-1325/N]

Volumn:

25

Issue:

2009 4

Page:

549-551

Research Field:

Mathematics, Physics, Mechanics

Publishing date:

2009-12-30

Info

Title:

Infinitely many periodic solutionsfor second-order Hamiltonian systems

Author(s):

Yin Cuicui;  Zhang Fubao;  Huang Chengshan

Department of Mathematics, Southeast University, Nanjing 211189, China

Keywords:

variant fountain theorem;  second-order Hamiltonian system;  infinitely periodic solutions;  even functional

PACS:

O175

DOI:

10.3969/j.issn.1003-7985.2009.04.028

Abstract:

The existence of high energy periodic solutions for the second-order Hamiltonian system -ü(t)+A(t)u(t)=∇F(t, u(t))with convex and concave nonlinearities is studied, where F(t, u)=F₁1(t, u)+F₂2(t, u). Under the condition that F is an even functional, infinitely many solutions for it are obtained by the variant fountain theorem. The result is a complement for some known ones in the critical point theory.

References:

[1] Mawhin J, Williem M.Critical point theory and Hamiltonian systems [M].New York: Springer Verlag, 1989.
[2] Ding Y H.Existence and multiplicity results for homocilinic solutions to a class of Hamiltonian systems[J].Nonlinear Analysis, 1995, 25(11): 1095-1113.
[3] Bartsch T, Willem M.On an elliptic equation with concave and convex nonlinearities[J].Proc Amer Math Soc, 1995, 123(11): 3555-3561.
[4] Tang C L.Existence and multiplicity of periodic solutions for nonautonomous second-order systems[J].Nonlinear Anal TMA, 1998, 32(3): 299-304.
[5] Wang Z Q.On a superlinear elliptic equation [J].Ann Inst H Poincare Anal Nonlineaire, 1991, 8: 43-57.
[6] Tang C L, Wu X P.Notes on periodic solutions of subquadratic second-order Hamiltonian systems [J].J Math Anal Appl, 2003, 285(1): 8-16.
[7] Zou W M.Variant fountain theorems and their applications[J].Manuscripta Math, 2001, 104(3): 343-358.
[8] Zou W M.Infinitely many solutions for Hamiltonian systems[J].J Differential Equations, 2002, 186(1): 141-164.
[9] Tang C L, Wu X P.Periodic solutions for a class of nonautonomous subquadratic second-order Hamiltonian systems[J].J Math Anal Appl, 2002, 275(2): 870-882.
[10] Zou W M, Schechter M.Critical point theory and its applications [M].New York:Springer Verlag, 2006.

Memo

Memo:

Biographies: Yin Cuicui(1985—), female, graduate; Zhang Fubao(corresponding author), male, doctor, professor, 101009933@seu.edu.cn.
Citation: Yin Cuicui, Zhang Fubao, Huang Chengshan.Infinitely many periodic solutions for second-order Hamiltonian systems[J].Journal of Southeast University(English Edition), 2009, 25(4): 549-551.

Common functions