## Abstract

This paper is concerned with the following system

with the Dirichlet boundary condition

Some results are obtained for the existence, multiplicity and nonexistence 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.

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Zhang, R. Positive solutions of BVPs for third-order discrete nonlinear difference systems.
*J. Appl. Math. Comput.* **35**, 551–575 (2011). https://doi.org/10.1007/s12190-010-0378-7

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DOI: https://doi.org/10.1007/s12190-010-0378-7