Homoclinic orbits and periodic solutions for a class of Hamiltonian systems on time scales

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:411

Article

Su, Youhui¹  Feng, Zhaosheng² 

[1] Xuzhou Inst Technol, Dept Math, Xuzhou 221116, Peoples R China

[2] Univ Texas Pan Amer, Dept Math, Edinburg, TX 78539 USA

关键词: Variational method;    Time scales;    Hamiltonian system;    Homoclinic orbit;    Periodic solutions;    Critical-point theorem;   

DOI  :  10.1016/j.jmaa.2013.08.068

来源: Elsevier

【 摘 要 】

In this paper, we are concerned with a second order non-autonomous Hamiltonian system on time scales T u(Delta Delta)(rho(t)) + V-u(t, u(t)) = f (t), t is an element of T-kappa Under certain conditions, the existence and multiplicity of periodic solutions are obtained for this Hamiltonian system on time scales by using the saddle point theory, the least action principle as well as the three-critical-point theorem. In addition, the existence of homoclinic orbit is obtained as a limit of 2kT-periodic solutions of a given sequence of Hamiltonian system on time scales by means of the mountain pass theorem and the standard minimizing argument. (C) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

Free