数学物理学报(英文版) ›› 2014, Vol. 34 ›› Issue (4): 1225-1236.doi: 10.1016/S0252-9602(14)60081-3

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SOLUTIONS TO DISCRETE MULTIPARAMETER PERIODIC BOUNDARY VALUE PROBLEMS INVOLVING THE p-LAPLACIAN VIA CRITICAL POINT THEORY

高承华   

  1. Department of Mathematics, Northwest Normal University, Lanzhou 730070, China
  • 出版日期:2014-07-20 发布日期:2014-07-20
  • 基金资助:

    Supported by NSFC (11326127, 11101335), NWNU-LKQN-11-23 and the Fundamental Research Funds for the Gansu Universities.

SOLUTIONS TO DISCRETE MULTIPARAMETER PERIODIC BOUNDARY VALUE PROBLEMS INVOLVING THE p-LAPLACIAN VIA CRITICAL POINT THEORY

 GAO Cheng-Hua   

  1. Department of Mathematics, Northwest Normal University, Lanzhou 730070, China
  • Online:2014-07-20 Published:2014-07-20
  • Supported by:

    Supported by NSFC (11326127, 11101335), NWNU-LKQN-11-23 and the Fundamental Research Funds for the Gansu Universities.

摘要:

In this paper, we consider the existence of three nontrivial solutions for a discrete non-linear multiparameter periodic problem involving the p-Laplacian. By using the similar method for the Dirichlet boundary value problems in [G. Bonanno and P. Candito, Appl. Anal., 88(4) (2009), pp. 605-616], we construct two new strong maximum principles and obtain that the boundary value problem has three positive solutions for  and μ in some suitable intervals. The approaches we use are the critical point theory.

关键词: discrete periodic boundary value problem, p-Laplacian, multiparameter, three solutions, critical point theory

Abstract:

In this paper, we consider the existence of three nontrivial solutions for a discrete non-linear multiparameter periodic problem involving the p-Laplacian. By using the similar method for the Dirichlet boundary value problems in [G. Bonanno and P. Candito, Appl. Anal., 88(4) (2009), pp. 605-616], we construct two new strong maximum principles and obtain that the boundary value problem has three positive solutions for  and μ in some suitable intervals. The approaches we use are the critical point theory.

Key words: discrete periodic boundary value problem, p-Laplacian, multiparameter, three solutions, critical point theory

中图分类号: 

  • 39A23