Articles

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

  • GAO Cheng-Hua
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  • Department of Mathematics, Northwest Normal University, Lanzhou 730070, China

Online published: 2014-07-20

Supported by

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

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.

Cite this article

GAO Cheng-Hua . SOLUTIONS TO DISCRETE MULTIPARAMETER PERIODIC BOUNDARY VALUE PROBLEMS INVOLVING THE p-LAPLACIAN VIA CRITICAL POINT THEORY[J]. Acta mathematica scientia, Series B, 2014 , 34(4) : 1225 -1236 . DOI: 10.1016/S0252-9602(14)60081-3

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