Positive Solutions of a Singular Positone and Semipositone Boundary Value Problems for Fourth-Order Difference Equations
This paper studies the boundary value problems for the fourth-order nonlinear singular difference equations Δ4u(i−2)=λα(i)f(i,u(i)), i∈[2,T+2], u(0)=u(1)=0, u(T+3)=u(T+4)=0. We show the existence of positive solutions for positone and semipositone type. The nonlinear term may be singular. Two exampl...
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| Format: | Article |
| Language: | English |
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Wiley
2010-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2010/312864 |
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| _version_ | 1849682911394004992 |
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| author | Chengjun Yuan |
| author_facet | Chengjun Yuan |
| author_sort | Chengjun Yuan |
| collection | DOAJ |
| description | This paper studies the boundary value problems for the fourth-order nonlinear singular difference equations Δ4u(i−2)=λα(i)f(i,u(i)), i∈[2,T+2], u(0)=u(1)=0, u(T+3)=u(T+4)=0. We show the existence of positive solutions for positone and semipositone type. The nonlinear term may be singular. Two examples are also given to illustrate the main results. The arguments are based upon fixed point theorems in a cone. |
| format | Article |
| id | doaj-art-d22f7afa43fd43e1808ca91cefa7a041 |
| institution | DOAJ |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2010-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-d22f7afa43fd43e1808ca91cefa7a0412025-08-20T03:24:02ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2010-01-01201010.1155/2010/312864312864Positive Solutions of a Singular Positone and Semipositone Boundary Value Problems for Fourth-Order Difference EquationsChengjun Yuan0School of Mathematics and Statistics, Northeast Normal University, Changchun 130024, ChinaThis paper studies the boundary value problems for the fourth-order nonlinear singular difference equations Δ4u(i−2)=λα(i)f(i,u(i)), i∈[2,T+2], u(0)=u(1)=0, u(T+3)=u(T+4)=0. We show the existence of positive solutions for positone and semipositone type. The nonlinear term may be singular. Two examples are also given to illustrate the main results. The arguments are based upon fixed point theorems in a cone.http://dx.doi.org/10.1155/2010/312864 |
| spellingShingle | Chengjun Yuan Positive Solutions of a Singular Positone and Semipositone Boundary Value Problems for Fourth-Order Difference Equations Discrete Dynamics in Nature and Society |
| title | Positive Solutions of a Singular Positone and Semipositone Boundary Value Problems for Fourth-Order Difference Equations |
| title_full | Positive Solutions of a Singular Positone and Semipositone Boundary Value Problems for Fourth-Order Difference Equations |
| title_fullStr | Positive Solutions of a Singular Positone and Semipositone Boundary Value Problems for Fourth-Order Difference Equations |
| title_full_unstemmed | Positive Solutions of a Singular Positone and Semipositone Boundary Value Problems for Fourth-Order Difference Equations |
| title_short | Positive Solutions of a Singular Positone and Semipositone Boundary Value Problems for Fourth-Order Difference Equations |
| title_sort | positive solutions of a singular positone and semipositone boundary value problems for fourth order difference equations |
| url | http://dx.doi.org/10.1155/2010/312864 |
| work_keys_str_mv | AT chengjunyuan positivesolutionsofasingularpositoneandsemipositoneboundaryvalueproblemsforfourthorderdifferenceequations |