Multiple Positive Solutions of a Second Order Nonlinear Semipositone m-Point Boundary Value Problem on Time Scales
In this paper, we study a general second-order m-point boundary value problem for nonlinear singular dynamic equation on time scales uΔ∇(t)+a(t)uΔ(t)+b(t)u(t)+λq(t)f(t,u(t))=0, t∈(0,1)𝕋, u(ρ(0))=0, u(σ(1))=∑i=1m-2αiu(ηi). This paper shows the existence of multiple positive solutions if f...
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| Format: | Article |
| Language: | English |
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Wiley
2010-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2010/261741 |
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| _version_ | 1832552675425648640 |
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| author | Chengjun Yuan Yongming Liu |
| author_facet | Chengjun Yuan Yongming Liu |
| author_sort | Chengjun Yuan |
| collection | DOAJ |
| description | In this paper, we study a general second-order m-point boundary value problem for nonlinear singular dynamic equation on time scales uΔ∇(t)+a(t)uΔ(t)+b(t)u(t)+λq(t)f(t,u(t))=0, t∈(0,1)𝕋, u(ρ(0))=0, u(σ(1))=∑i=1m-2αiu(ηi). This paper shows the existence of multiple positive solutions if f is semipositone and superlinear. The arguments are based upon fixed-point theorems in a cone. |
| format | Article |
| id | doaj-art-e8d10dc5f1c54e09869cc5506639b837 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2010-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-e8d10dc5f1c54e09869cc5506639b8372025-02-03T05:58:14ZengWileyAbstract and Applied Analysis1085-33751687-04092010-01-01201010.1155/2010/261741261741Multiple Positive Solutions of a Second Order Nonlinear Semipositone m-Point Boundary Value Problem on Time ScalesChengjun Yuan0Yongming Liu1Department of Mathematics, East China Normal University, Shanghai 200241, ChinaDepartment of Mathematics, East China Normal University, Shanghai 200241, ChinaIn this paper, we study a general second-order m-point boundary value problem for nonlinear singular dynamic equation on time scales uΔ∇(t)+a(t)uΔ(t)+b(t)u(t)+λq(t)f(t,u(t))=0, t∈(0,1)𝕋, u(ρ(0))=0, u(σ(1))=∑i=1m-2αiu(ηi). This paper shows the existence of multiple positive solutions if f is semipositone and superlinear. The arguments are based upon fixed-point theorems in a cone.http://dx.doi.org/10.1155/2010/261741 |
| spellingShingle | Chengjun Yuan Yongming Liu Multiple Positive Solutions of a Second Order Nonlinear Semipositone m-Point Boundary Value Problem on Time Scales Abstract and Applied Analysis |
| title | Multiple Positive Solutions of a Second Order Nonlinear Semipositone m-Point Boundary Value Problem on Time Scales |
| title_full | Multiple Positive Solutions of a Second Order Nonlinear Semipositone m-Point Boundary Value Problem on Time Scales |
| title_fullStr | Multiple Positive Solutions of a Second Order Nonlinear Semipositone m-Point Boundary Value Problem on Time Scales |
| title_full_unstemmed | Multiple Positive Solutions of a Second Order Nonlinear Semipositone m-Point Boundary Value Problem on Time Scales |
| title_short | Multiple Positive Solutions of a Second Order Nonlinear Semipositone m-Point Boundary Value Problem on Time Scales |
| title_sort | multiple positive solutions of a second order nonlinear semipositone m point boundary value problem on time scales |
| url | http://dx.doi.org/10.1155/2010/261741 |
| work_keys_str_mv | AT chengjunyuan multiplepositivesolutionsofasecondordernonlinearsemipositonempointboundaryvalueproblemontimescales AT yongmingliu multiplepositivesolutionsofasecondordernonlinearsemipositonempointboundaryvalueproblemontimescales |