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

Authors : Tianlan CHEN, Ruyun MA, Yongwen LIANG

Pages : 2371-2379

View : 10 | Download : 7

Publication Date : 0000-00-00

Article Type : Research Paper

Abstract :We show existence results of positive solutions of Neumann problems for a discrete system: $$\aligned &\eta\Delta^2insert ignore into journalissuearticles values(A_{k-1}-A^0_{k-1});-A_{k}+A^0_{k}+N_kA_{k}=0,\ \ k\in[2, n-1]_\mathbb{Z},\\ &\Delta\biginsert ignore into journalissuearticles values(\Delta N_{k-1}-2N_k\frac{\Delta A_{k-1}}{A_{k}}\big);-N_kA_{k}+A^1_{k}-A^0_{k}=0,\ \ k\in[2, n-1]_\mathbb{Z},\\ &\Delta A_{1}=0=\Delta A_{n-1},\ \ \Delta N_{1}=0=\Delta N_{n-1}, \endaligned $$ 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