数学物理学报(英文版) ›› 2010, Vol. 30 ›› Issue (1): 341-349.doi: 10.1016/S0252-9602(10)60051-3

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MULTIPLE SOLUTIONS FOR NONAUTONOMOUS SECOND ORDER PERIODIC SYSTEMS

  

  1. Institute of Computer Science, Jagiellonian University,  ul. Nawojki 11, Cracow |30072, Poland
  • 收稿日期:2006-04-29 修回日期:2008-09-26 出版日期:2010-01-20 发布日期:2010-01-20
  • 基金资助:

    This research has been partially supported by the State Committee for Scientific Research of Poland (KBN) under research grants nr. 2 P03A 003 25 and nr. 4 T07A 027 26.

MULTIPLE SOLUTIONS FOR NONAUTONOMOUS SECOND ORDER PERIODIC SYSTEMS

  1. Institute of Computer Science, Jagiellonian University,  ul. Nawojki 11, Cracow |30072, Poland
  • Received:2006-04-29 Revised:2008-09-26 Online:2010-01-20 Published:2010-01-20
  • Supported by:

    This research has been partially supported by the State Committee for Scientific Research of Poland (KBN) under research grants nr. 2 P03A 003 25 and nr. 4 T07A 027 26.

摘要:

We study nonautonomonus second order periodic systems with a nonsmooth potential. Using the nonsmooth critical theory, we establish the existence of at least two nontrivial solutions. Our framework incorporates large classes of both subquadratic and superquadratic potentials at infinity.

关键词: locally Lipschitz potential,  generalized subdifferential,  coercive functional,  critical point,  local linking theorem,   , nonsmooth Palais-Smale condition,  multiple nontrivial solutions

Abstract:

We study nonautonomonus second order periodic systems with a nonsmooth potential. Using the nonsmooth critical theory, we establish the existence of at least two nontrivial solutions. Our framework incorporates large classes of both subquadratic and superquadratic potentials at infinity.

Key words: locally Lipschitz potential,  generalized subdifferential,  coercive functional,  critical point,  local linking theorem,   , nonsmooth Palais-Smale condition,  multiple nontrivial solutions

中图分类号: 

  • 34C25