Existence of positive solutions for difference systems coming from   a model for  burglary

Tianlan CHEN; Ruyun MA

Article Details

Existence of positive solutions for difference systems coming from a model for burglary

Authors:

Tianlan CHEN | Ruyun MA

Publisher:

TUBITAK

Journal:

Turkish Journal of Mathematics 2016 Vol.40 Issue 5, pp.1049-1057

Document Type:

Article

Publication Date:

9/2016

Document Language:

Turkish

Document ID (Org No.):

2000746130

Frequency:

Bimonthly

eISSN:

1303-6149

pISSN:

1300-0098

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\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\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, Dk,A0k,fw, Dk,Ak0,fw,\ D_k, A_k^0, f, and ggg are motivated  by some mathematical models for the burglary of  houses.

Article Details

Existence of positive solutions for difference systems coming from a model for burglary

Authors: Tianlan CHEN | Ruyun MA

Publisher: TUBITAK

Journal: Turkish Journal of Mathematics 2016 Vol.40 Issue 5, pp.1049-1057

Document Type: Article

Publication Date: 9/2016

Document Language: Turkish

Document ID (Org No.): 2000746130

Frequency: Bimonthly

eISSN: 1303-6149

pISSN: 1300-0098

Issues

Authors:

Tianlan CHEN | Ruyun MA

Publisher:

TUBITAK

Journal:

Turkish Journal of Mathematics 2016 Vol.40 Issue 5, pp.1049-1057

Document Type:

Article

Publication Date:

9/2016

Document Language:

Turkish

Document ID (Org No.):

2000746130

Frequency:

Bimonthly

eISSN:

1303-6149

pISSN:

1300-0098