Necessary and Sufficient Condition for the Existence of Solutions to a Discrete Second-Order Boundary Value Problem
This paper is concerned with the existence of solutions for the discrete second-order boundary value problem Δ2u(t-1)+λ1u(t)+g(Δu(t))=f(t), t∈{1,2,…,T}, u(0)=u(T+1)=0, where T>1 is an integer, f:{1,…,T}→R, g:R→R is bounded and continuous, and λ1 is the first eigenvalue of the eigenvalue problem Δ...
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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/10.1155/2012/951251 |
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| _version_ | 1832553359939207168 |
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| author | Chenghua Gao |
| author_facet | Chenghua Gao |
| author_sort | Chenghua Gao |
| collection | DOAJ |
| description | This paper is concerned with the existence of solutions for the discrete second-order boundary value problem Δ2u(t-1)+λ1u(t)+g(Δu(t))=f(t), t∈{1,2,…,T}, u(0)=u(T+1)=0, where T>1 is an integer, f:{1,…,T}→R, g:R→R is bounded and continuous, and λ1 is the first eigenvalue of the eigenvalue problem Δ2u(t-1)+λu(t)=0, t∈T, u(0)=u(T+1)=0. |
| format | Article |
| id | doaj-art-ce87d9ca56c549a9832274eb96d2cd9d |
| 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-ce87d9ca56c549a9832274eb96d2cd9d2025-02-03T05:54:16ZengWileyAbstract and Applied Analysis1085-33751687-04092012-01-01201210.1155/2012/951251951251Necessary and Sufficient Condition for the Existence of Solutions to a Discrete Second-Order Boundary Value ProblemChenghua Gao0Department of Mathematics, Northwest Normal University, Lanzhou 730070, ChinaThis paper is concerned with the existence of solutions for the discrete second-order boundary value problem Δ2u(t-1)+λ1u(t)+g(Δu(t))=f(t), t∈{1,2,…,T}, u(0)=u(T+1)=0, where T>1 is an integer, f:{1,…,T}→R, g:R→R is bounded and continuous, and λ1 is the first eigenvalue of the eigenvalue problem Δ2u(t-1)+λu(t)=0, t∈T, u(0)=u(T+1)=0.http://dx.doi.org/10.1155/2012/951251 |
| spellingShingle | Chenghua Gao Necessary and Sufficient Condition for the Existence of Solutions to a Discrete Second-Order Boundary Value Problem Abstract and Applied Analysis |
| title | Necessary and Sufficient Condition for the Existence of Solutions to a Discrete Second-Order Boundary Value Problem |
| title_full | Necessary and Sufficient Condition for the Existence of Solutions to a Discrete Second-Order Boundary Value Problem |
| title_fullStr | Necessary and Sufficient Condition for the Existence of Solutions to a Discrete Second-Order Boundary Value Problem |
| title_full_unstemmed | Necessary and Sufficient Condition for the Existence of Solutions to a Discrete Second-Order Boundary Value Problem |
| title_short | Necessary and Sufficient Condition for the Existence of Solutions to a Discrete Second-Order Boundary Value Problem |
| title_sort | necessary and sufficient condition for the existence of solutions to a discrete second order boundary value problem |
| url | http://dx.doi.org/10.1155/2012/951251 |
| work_keys_str_mv | AT chenghuagao necessaryandsufficientconditionfortheexistenceofsolutionstoadiscretesecondorderboundaryvalueproblem |