Turkish Journal of Mathematics
DOI
10.3906/mat-1506-59
Abstract
In this paper, we use the Brouwer degree to prove existence results of positive solutions for the following difference systems: $$\aligned &{D}_k\Delta^2(A_{k-1}-A^0_{k-1})-(A_{k}-A^0_{k})+N_kf(k, A_{k})=0,\ \ k\in[2, n-1]_\mathbb{Z},\\ &\Delta^2N_{k-1}+\Delta[g(k, A_{k}, \Delta A_{k-1})N_k]-w^2(N_k-1)=0,\ \ k\in[2, n-1]_\mathbb{Z},\\ &\Delta A_{1}=0=\Delta A_{n-1},\ \ \Delta N_{1}=0=\Delta N_{n-1}, \endaligned\eqno $$ where the assumptions on $w,\ D_k, A_k^0, f$, and $g$ are motivated by some mathematical models for the burglary of houses.
Keywords
Neumann problems, Brouwer degree, positive solution, models for house burglary
First Page
1049
Last Page
1057
Recommended Citation
CHEN, TIANLAN and MA, RUYUN
(2016)
"Existence of positive solutions for difference systems coming from a model for burglary,"
Turkish Journal of Mathematics: Vol. 40:
No.
5, Article 11.
https://doi.org/10.3906/mat-1506-59
Available at:
https://journals.tubitak.gov.tr/math/vol40/iss5/11
