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

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Published: Dec 30, 2015
Keywords:
One-dimension Laplacian, bilateral difference system, boundary value problem, positive solution, homoclinic solution, fixed point theorem
Mathematics Subject Classification:
39A11, 34B10, 34B15

Main Article Content

Xiaohui Yang
Department of Computers Guangdong Police College Guangzhou 510230, P. R. China}
Yuji Liu
Department of Mathematics and Statics Guangdong University of Finance andEconomics Guangzhou 510320, P. R.China

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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