Existence of positive solutions of BVPs for third-order discrete nonlinear difference systems

In this paper we consider the following boundary value problem of discrete [email protected]^3u"1(k)+f"1(k,u"1(k),u"2(k))=0,[email protected]?[0,T],@D^3u"2(k)+f"2(k,u"1(k),u"2(k))=0,[email protected]?[0,T],with the Dirichlet boundary conditionu"1(0)=u"1(1)=u"1(T+3)=0=u"2(0)=u"2(1)=u"2(T+3).Some new results of the existence, nonexistence and multiplicity are obtained by using Krasnosel'skii's fixed point theorem in a cone. In particular, it is proved that the above boundary value problem has N positive solutions under suitable conditions, where N is an arbitrary positive integer.

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