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Existence of positive solutions of BVPs for second-order nonlinear difference systems. (English) Zbl 1077.39001

This paper is concerned with the following system

Δu i (k)+f i (k,u 1 (k),u 2 (k),,u n (k))=0,k[0,T],i=1,2,,n

with the Dirichlet boundary condition u i (0)=u i (T+2)=0, i=1,2,,n. Some new results are obtained for the existence and multiplicity of positive solutions to the above system by using nonlinear alternative of Leray-Schauder type, Krasnosel’skii’s fixed point theorem in a cone and Leggett-Williams fixed point theorem. In particular, it proves that the above system has N positive solutions under suitable conditions, where N is an arbitrary integer.

39A05General theory of difference equations