Journal of South China University of Technology (Natural Science Edition) ›› 2005, Vol. 33 ›› Issue (10): 103-107.

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Existence of Infinitely Many Solutions to the Quasilinear Subelliptic Equations on Heisenberg Group

He Chun-xiong  Chen Shu-min  Yao Yang-xin   

  1. College of Mathematical Sciences,South China Univ.ofTech.,Guangzhou 510640,Guangdong,China
  • Received:2004-07-28 Online:2005-10-25 Published:2005-10-25
  • Contact: 何春雄(1958-)，男，博士，教授，主要从事偏微分方程及其应用、随机分析和金融数学等方面的研究． E-mail:machxhe@ scut.edu.ca
  • About author:何春雄(1958-)，男，博士，教授，主要从事偏微分方程及其应用、随机分析和金融数学等方面的研究．
  • Supported by:

    国家自然科学基金资助项目(10171032)

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Abstract:

The existence for the solutions to the quasilinear subelliptic partial differential equations in a weighted Sobolev space is investigated in the condition that the nonlinear term is odd. Under comparably weaker conditions,the corresponding functional is proved to satisfy the Cerami condition. Moreover,by using the Fountain theorem of Bartsch,the existence of infinitely many solutions with large energy for the equations are obtained.

Key words: Heisenberg group, quasilinearity, subelliptic equation, Cerami condition, Fountain theorem, weigh-ted Sobolev space