Positive Solutions of the One-Dimensional p-Laplacian with Nonlinearity Defined on a Finite Interval
We use the quadrature method to show the existence and multiplicity of positive solutions of the boundary value problems involving one-dimensional p-Laplacian u′t|p−2u′t′+λfut=0, t∈0,1, u(0)=u(1)=0, where p∈(1,2], λ∈(0,∞) is a parameter, f∈C1([0,r),[0,∞)) for some constant r>0, f(s)>0 in (0,r)...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2013/492026 |
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| _version_ | 1832557105214652416 |
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| author | Ruyun Ma Chunjie Xie Abubaker Ahmed |
| author_facet | Ruyun Ma Chunjie Xie Abubaker Ahmed |
| author_sort | Ruyun Ma |
| collection | DOAJ |
| description | We use the quadrature method to show the existence and multiplicity of positive solutions of the boundary value problems involving one-dimensional p-Laplacian u′t|p−2u′t′+λfut=0, t∈0,1, u(0)=u(1)=0, where p∈(1,2], λ∈(0,∞) is a parameter, f∈C1([0,r),[0,∞)) for some constant r>0, f(s)>0 in (0,r), and lims→r-(r-s)p-1f(s)=+∞. |
| format | Article |
| id | doaj-art-74df9a6859d64462b1574583939b48a9 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-74df9a6859d64462b1574583939b48a92025-02-03T05:43:42ZengWileyAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/492026492026Positive Solutions of the One-Dimensional p-Laplacian with Nonlinearity Defined on a Finite IntervalRuyun Ma0Chunjie Xie1Abubaker Ahmed2Department of Mathematics, Northwest Normal University, Lanzhou 730070, ChinaDepartment of Mathematics, Northwest Normal University, Lanzhou 730070, ChinaDepartment of Mathematics, Northwest Normal University, Lanzhou 730070, ChinaWe use the quadrature method to show the existence and multiplicity of positive solutions of the boundary value problems involving one-dimensional p-Laplacian u′t|p−2u′t′+λfut=0, t∈0,1, u(0)=u(1)=0, where p∈(1,2], λ∈(0,∞) is a parameter, f∈C1([0,r),[0,∞)) for some constant r>0, f(s)>0 in (0,r), and lims→r-(r-s)p-1f(s)=+∞.http://dx.doi.org/10.1155/2013/492026 |
| spellingShingle | Ruyun Ma Chunjie Xie Abubaker Ahmed Positive Solutions of the One-Dimensional p-Laplacian with Nonlinearity Defined on a Finite Interval Abstract and Applied Analysis |
| title | Positive Solutions of the One-Dimensional p-Laplacian with Nonlinearity Defined on a Finite Interval |
| title_full | Positive Solutions of the One-Dimensional p-Laplacian with Nonlinearity Defined on a Finite Interval |
| title_fullStr | Positive Solutions of the One-Dimensional p-Laplacian with Nonlinearity Defined on a Finite Interval |
| title_full_unstemmed | Positive Solutions of the One-Dimensional p-Laplacian with Nonlinearity Defined on a Finite Interval |
| title_short | Positive Solutions of the One-Dimensional p-Laplacian with Nonlinearity Defined on a Finite Interval |
| title_sort | positive solutions of the one dimensional p laplacian with nonlinearity defined on a finite interval |
| url | http://dx.doi.org/10.1155/2013/492026 |
| work_keys_str_mv | AT ruyunma positivesolutionsoftheonedimensionalplaplacianwithnonlinearitydefinedonafiniteinterval AT chunjiexie positivesolutionsoftheonedimensionalplaplacianwithnonlinearitydefinedonafiniteinterval AT abubakerahmed positivesolutionsoftheonedimensionalplaplacianwithnonlinearitydefinedonafiniteinterval |