Korean J. Math. Vol. 23 No. 4 (2015) pp.665-732
DOI: https://doi.org/10.11568/kjm.2015.23.4.665

# Studies on boundary value problems for bilateral difference systems with one-dimensional Laplacians

## Abstract

Existence results for multiple positive solutions of two classes of boundary value problems for bilateral difference systems are established by using a fixed point theorem under convenient assumptions. It is the purpose of this paper to show that the approach to get positive solutions of boundary value problems of finite difference equations by using multi-fixed-point theorems can be extended to treat the bilateral difference systems with one-dimensional Laplacians. As an application, the sufficient conditions are established for finding multiple positive homoclinic solutions of a bilateral difference system. The methods used in this paper may be useful for numerical simulation. An example is presented to illustrate the main theorems. Further studies are proposed at the end of the paper.

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