Eventually Periodic Solutions for Difference Equations with Periodic Coefficients and Nonlinear Control Functions
For nonlinear difference equations of the form xn=F(n,xn−1,…,xn−m), it is usually difficult to find periodic solutions. In this paper, we consider a class of difference equations of the form xn=anxn−1+bnf(xn−k), where {an}, {bn} are periodic sequences and f is a nonlinear filtering function, and sh...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2008-01-01
|
| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2008/179589 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832551499200200704 |
|---|---|
| author | Chengmin Hou Sui Sun Cheng |
| author_facet | Chengmin Hou Sui Sun Cheng |
| author_sort | Chengmin Hou |
| collection | DOAJ |
| description | For nonlinear difference equations of the form xn=F(n,xn−1,…,xn−m), it is usually difficult to find periodic solutions. In this paper, we consider a class of difference equations of the form xn=anxn−1+bnf(xn−k), where {an}, {bn} are periodic sequences and f is a nonlinear filtering function, and show how periodic solutions can be constructed. Several examples are also included to illustrate our results. |
| format | Article |
| id | doaj-art-df36bea0b3fa401fad6e860c5b68cad1 |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2008-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-df36bea0b3fa401fad6e860c5b68cad12025-02-03T06:01:28ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2008-01-01200810.1155/2008/179589179589Eventually Periodic Solutions for Difference Equations with Periodic Coefficients and Nonlinear Control FunctionsChengmin Hou0Sui Sun Cheng1Department of Mathematics, Yanbian University, Yanji 133002, ChinaDepartment of Mathematics, Tsing Hua University, Hsinchu 30043, TaiwanFor nonlinear difference equations of the form xn=F(n,xn−1,…,xn−m), it is usually difficult to find periodic solutions. In this paper, we consider a class of difference equations of the form xn=anxn−1+bnf(xn−k), where {an}, {bn} are periodic sequences and f is a nonlinear filtering function, and show how periodic solutions can be constructed. Several examples are also included to illustrate our results.http://dx.doi.org/10.1155/2008/179589 |
| spellingShingle | Chengmin Hou Sui Sun Cheng Eventually Periodic Solutions for Difference Equations with Periodic Coefficients and Nonlinear Control Functions Discrete Dynamics in Nature and Society |
| title | Eventually Periodic Solutions for Difference Equations with Periodic Coefficients and Nonlinear Control Functions |
| title_full | Eventually Periodic Solutions for Difference Equations with Periodic Coefficients and Nonlinear Control Functions |
| title_fullStr | Eventually Periodic Solutions for Difference Equations with Periodic Coefficients and Nonlinear Control Functions |
| title_full_unstemmed | Eventually Periodic Solutions for Difference Equations with Periodic Coefficients and Nonlinear Control Functions |
| title_short | Eventually Periodic Solutions for Difference Equations with Periodic Coefficients and Nonlinear Control Functions |
| title_sort | eventually periodic solutions for difference equations with periodic coefficients and nonlinear control functions |
| url | http://dx.doi.org/10.1155/2008/179589 |
| work_keys_str_mv | AT chengminhou eventuallyperiodicsolutionsfordifferenceequationswithperiodiccoefficientsandnonlinearcontrolfunctions AT suisuncheng eventuallyperiodicsolutionsfordifferenceequationswithperiodiccoefficientsandnonlinearcontrolfunctions |