Positive Solutions of a General Discrete Dirichlet Boundary Value Problem
A steady state equation of the discrete heat diffusion can be obtained by the heat diffusion of particles or the difference method of the elliptic equations. In this paper, the nonexistence, existence, and uniqueness of positive solutions for a general discrete Dirichlet boundary value problem are c...
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| Format: | Article |
| Language: | English |
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Wiley
2016-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2016/7456937 |
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| _version_ | 1832561115686502400 |
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| author | Xinfu Li Guang Zhang |
| author_facet | Xinfu Li Guang Zhang |
| author_sort | Xinfu Li |
| collection | DOAJ |
| description | A steady state equation of the discrete heat diffusion can be obtained by the heat diffusion of particles or the difference method of the elliptic equations. In this paper, the nonexistence, existence, and uniqueness of positive solutions for a general discrete Dirichlet boundary value problem are considered by using the maximum principle, eigenvalue method, sub- and supersolution technique, and monotone method. All obtained results are new and valid on any n-dimension finite lattice point domain. To the best of our knowledge, they are better than the results of the corresponding partial differential equations. In particular, the methods of proof are different. |
| format | Article |
| id | doaj-art-cdf14647873e4076b085ad8807241f79 |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2016-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-cdf14647873e4076b085ad8807241f792025-02-03T01:26:00ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2016-01-01201610.1155/2016/74569377456937Positive Solutions of a General Discrete Dirichlet Boundary Value ProblemXinfu Li0Guang Zhang1School of Science, Tianjin University of Commerce, Tianjin 300134, ChinaSchool of Science, Tianjin University of Commerce, Tianjin 300134, ChinaA steady state equation of the discrete heat diffusion can be obtained by the heat diffusion of particles or the difference method of the elliptic equations. In this paper, the nonexistence, existence, and uniqueness of positive solutions for a general discrete Dirichlet boundary value problem are considered by using the maximum principle, eigenvalue method, sub- and supersolution technique, and monotone method. All obtained results are new and valid on any n-dimension finite lattice point domain. To the best of our knowledge, they are better than the results of the corresponding partial differential equations. In particular, the methods of proof are different.http://dx.doi.org/10.1155/2016/7456937 |
| spellingShingle | Xinfu Li Guang Zhang Positive Solutions of a General Discrete Dirichlet Boundary Value Problem Discrete Dynamics in Nature and Society |
| title | Positive Solutions of a General Discrete Dirichlet Boundary Value Problem |
| title_full | Positive Solutions of a General Discrete Dirichlet Boundary Value Problem |
| title_fullStr | Positive Solutions of a General Discrete Dirichlet Boundary Value Problem |
| title_full_unstemmed | Positive Solutions of a General Discrete Dirichlet Boundary Value Problem |
| title_short | Positive Solutions of a General Discrete Dirichlet Boundary Value Problem |
| title_sort | positive solutions of a general discrete dirichlet boundary value problem |
| url | http://dx.doi.org/10.1155/2016/7456937 |
| work_keys_str_mv | AT xinfuli positivesolutionsofageneraldiscretedirichletboundaryvalueproblem AT guangzhang positivesolutionsofageneraldiscretedirichletboundaryvalueproblem |