Acta mathematica scientia,Series B ›› 2012, Vol. 32 ›› Issue (4): 1545-1558.doi: 10.1016/S0252-9602(12)60122-2

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NONTRIVIAL SOLUTIONS FOR ASYMPTOTICALLY LINEAR HAMILTONIAN SYSTEMS WITH LAGRANGIAN BOUNDARY CONDITIONS

 LIU Chun-Gen1, ZHANG Qing-Ye2   

  1. 1.School of Mathematical Science and LPMC, Nankai University, Tianjin 300071, China; 2.School of Mathematics and Information Sciences, Jiangxi Normal University, Nanchang 330022, China.
  • Received:2010-07-28 Online:2012-07-20 Published:2012-07-20
  • Supported by:

    Partially supported by NFS of China (11071127, 10621101) and 973 Program of STM (2011CB808002); Part work of this paper was completed when the second author studying in Nankai University for his PhD programm.

Abstract:

In this article, we study the existence of nontrivial solutions for a class of asymptotically linear Hamiltonian systems with Lagrangian boundary conditions by the Galerkin approximation methods and the L-index theory developed by the first author.

Key words: Lagrangian boundary conditions, Hamiltonian systems, asymptotically lin-ear, Maslov-type index

CLC Number: 

  • 34B10
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