Infinitely many periodic solutions for a class of second-order Hamiltonian systems

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• 作者：Ming-hai Yang ; Yue-fen Chen ; Yan-fang Xue
• 关键词：second ; order Hamiltonian systems ; periodic solutions ; Fountain theorem
• 刊名：Acta Mathematicae Applicatae Sinica, English Series
• 出版年：2016
• 出版时间：June 2016
• 年：2016
• 卷：32
• 期：1
• 页码：231-238
• 全文大小：215 KB
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• 作者单位：Ming-hai Yang (1)
  Yue-fen Chen (1)
  Yan-fang Xue (1)
  
  1. Department of Mathematics, Xinyang Normal University, Xinyang, 464000, China
  
• 刊物主题：Applications of Mathematics; Math Applications in Computer Science; Theoretical, Mathematical and Computational Physics;
• 出版者：Institute of Applied Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society
• ISSN：1618-3932

文摘

In this paper we study the existence of infinitely many periodic solutions for second-order Hamiltonian systems $$\left\{ {\begin{array}{*{20}c} {\ddot u(t) + A(t)u(t) + \nabla F(t,u(t)) = 0,} \\ {u(0) - u(T) = \dot u(0) - \dot u(T) = 0,} \\ \end{array} } \right. $$, where F(t, u) is even in u, and ∇F(t, u) is of sublinear growth at infinity and satisfies the Ahmad-Lazer-Paul condition. Keywords second-order Hamiltonian systems periodic solutions Fountain theorem 2000 MR Subject Classification 37J45 58E05 34C37 70H05 Supported by NSF of Education Committee of Henan province (12B11026) and NSF of Henan province (132300410341,122300410034,132300410056) and Nanhu Scholars Program for Young Scholars of XYNU.