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Turkish Journal of Mathematics

DOI

10.3906/mat-1805-11

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.

Keywords

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

First Page

2371

Last Page

2379

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