Existence of Bounded Positive Solutions for Partial Difference Equations with Delays
This paper deals with solvability of the third-order nonlinear partial difference equation with delays Δn(am,nΔm2(xm,n+bm,nxm-τ0,n-σ0))+f(m,n,xm-τ1,m,n-σ1,n,…,xm-τk,m,n-σk,n)=cm,n, m≥m0, n≥n0. With the help of the Banach fixed-point theorem, the existence results of uncountably many bounded positi...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2012/191254 |
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| _version_ | 1832550194825134080 |
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| author | Zeqing Liu Zhihua Wu Young Chel Kwun Shin Min Kang |
| author_facet | Zeqing Liu Zhihua Wu Young Chel Kwun Shin Min Kang |
| author_sort | Zeqing Liu |
| collection | DOAJ |
| description | This paper deals with solvability of the third-order nonlinear partial difference equation with delays Δn(am,nΔm2(xm,n+bm,nxm-τ0,n-σ0))+f(m,n,xm-τ1,m,n-σ1,n,…,xm-τk,m,n-σk,n)=cm,n, m≥m0, n≥n0. With the help of the Banach fixed-point theorem, the existence results of uncountably many bounded positive solutions for the partial difference equation are given; some Mann iterative schemes with errors are suggested, and the error estimates between the iterative schemes and the bounded positive solutions are discussed. Three nontrivial examples illustrating the results presented in this paper are also provided. |
| format | Article |
| id | doaj-art-1ad8cbbbb74242029811d72ada26057e |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-1ad8cbbbb74242029811d72ada26057e2025-02-03T06:07:24ZengWileyAbstract and Applied Analysis1085-33751687-04092012-01-01201210.1155/2012/191254191254Existence of Bounded Positive Solutions for Partial Difference Equations with DelaysZeqing Liu0Zhihua Wu1Young Chel Kwun2Shin Min Kang3Department of Mathematics, Liaoning Normal University, Dalian, Liaoning 116029, ChinaDepartment of Mathematics, Liaoning Normal University, Dalian, Liaoning 116029, ChinaDepartment of Mathematics, Dong-A University, Busan 614-714, Republic of KoreaDepartment of Mathematics and RINS, Gyeongsang National University, Jinju 660-701, Republic of KoreaThis paper deals with solvability of the third-order nonlinear partial difference equation with delays Δn(am,nΔm2(xm,n+bm,nxm-τ0,n-σ0))+f(m,n,xm-τ1,m,n-σ1,n,…,xm-τk,m,n-σk,n)=cm,n, m≥m0, n≥n0. With the help of the Banach fixed-point theorem, the existence results of uncountably many bounded positive solutions for the partial difference equation are given; some Mann iterative schemes with errors are suggested, and the error estimates between the iterative schemes and the bounded positive solutions are discussed. Three nontrivial examples illustrating the results presented in this paper are also provided.http://dx.doi.org/10.1155/2012/191254 |
| spellingShingle | Zeqing Liu Zhihua Wu Young Chel Kwun Shin Min Kang Existence of Bounded Positive Solutions for Partial Difference Equations with Delays Abstract and Applied Analysis |
| title | Existence of Bounded Positive Solutions for Partial Difference Equations with Delays |
| title_full | Existence of Bounded Positive Solutions for Partial Difference Equations with Delays |
| title_fullStr | Existence of Bounded Positive Solutions for Partial Difference Equations with Delays |
| title_full_unstemmed | Existence of Bounded Positive Solutions for Partial Difference Equations with Delays |
| title_short | Existence of Bounded Positive Solutions for Partial Difference Equations with Delays |
| title_sort | existence of bounded positive solutions for partial difference equations with delays |
| url | http://dx.doi.org/10.1155/2012/191254 |
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