Positive Solutions and Iterative Approximations for a Nonlinear Two-Dimensional Difference System with Multiple Delays
This paper studies the nonlinear two-dimensional difference system with multiple delays Δ(xn+p1nxn-τ1)+f1(n,xa1n,…,xahn,yb1n,…,ybkn)=q1n,Δ(yn+p2nyn-τ2)+f2(n,xc1n,…,xchn,yd1n,…,ydkn)=q2n,n≥n0. Using the Banach fixed point theorem and a few new analysis techniques, we show the existence of uncountably...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2012-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2012/240378 |
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| Summary: | This paper studies the nonlinear two-dimensional difference system with multiple delays Δ(xn+p1nxn-τ1)+f1(n,xa1n,…,xahn,yb1n,…,ybkn)=q1n,Δ(yn+p2nyn-τ2)+f2(n,xc1n,…,xchn,yd1n,…,ydkn)=q2n,n≥n0. Using the Banach fixed point theorem and a few new analysis techniques, we show the existence of uncountably many bounded positive solutions for the system, suggest Mann iterative algorithms with errors, and discuss
the error estimates between the positive solutions and iterative sequences generated by the Mann iterative
algorithms. Examples to illustrates the results are included. |
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| ISSN: | 1085-3375 1687-0409 |