Positive solutions of Neumann problems for a discrete system coming from models of house burglary

Authors

TIANLAN CHEN
RUYUN MA
YONGWEN LIANG

Abstract

We show existence results of positive solutions of Neumann problems for a discrete system: $$\aligned &\eta\Delta^2(A_{k-1}-A^0_{k-1})-A_{k}+A^0_{k}+N_kA_{k}=0,\ \ k\in[2, n-1]_\mathbb{Z},\\ &\Delta\big(\Delta N_{k-1}-2N_k\frac{\Delta A_{k-1}}{A_{k}}\big)-N_kA_{k}+A^1_{k}-A^0_{k}=0,\ \ k\in[2, n-1]_\mathbb{Z},\\ &\Delta A_{1}=0=\Delta A_{n-1},\ \ \Delta N_{1}=0=\Delta N_{n-1}, \endaligned $$ where the assumptions on $\eta,\ A_k^0$, and $A_k^1$ are motivated by some mathematics models for house burglary. Our results are based on the topological degree theory.

DOI

10.3906/mat-1805-11

Keywords

Neumann boundary value problems, nonconstant positive solutions, topological degree theory

First Page

2371

Last Page

2379

Recommended Citation

CHEN, TIANLAN; MA, RUYUN; and LIANG, YONGWEN (2018) "Positive solutions of Neumann problems for a discrete system coming from models of house burglary," Turkish Journal of Mathematics: Vol. 42: No. 5, Article 21. https://doi.org/10.3906/mat-1805-11
Available at: https://journals.tubitak.gov.tr/math/vol42/iss5/21