Multiplicity of Positive Solutions for a Singular Second-Order Three-Point Boundary Value Problem with a Parameter
This paper is concerned with the following second-order three-point boundary value problem u″t+β2ut+λqtft,ut=0, t∈0 , 1, u0=0, u(1)=δu(η), where β∈(0,π/2), δ>0, η∈(0,1), and λ is a positive parameter. First, Green’s function for the associated linear boundary value problem is constructed, and the...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2014/603203 |
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| _version_ | 1832550549080244224 |
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| author | Jian Liu Hanying Feng Xingfang Feng |
| author_facet | Jian Liu Hanying Feng Xingfang Feng |
| author_sort | Jian Liu |
| collection | DOAJ |
| description | This paper is concerned with the following second-order three-point boundary value problem u″t+β2ut+λqtft,ut=0, t∈0 , 1, u0=0, u(1)=δu(η), where β∈(0,π/2), δ>0, η∈(0,1), and λ is a positive parameter. First, Green’s function for the associated linear boundary value problem is constructed, and then some useful properties of Green’s function are obtained. Finally, existence, multiplicity, and nonexistence results for positive solutions are derived in terms of different values of λ by means of the fixed point index theory. |
| format | Article |
| id | doaj-art-49b1440f1612498f817ebae50914e32f |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-49b1440f1612498f817ebae50914e32f2025-02-03T06:06:25ZengWileyJournal of Applied Mathematics1110-757X1687-00422014-01-01201410.1155/2014/603203603203Multiplicity of Positive Solutions for a Singular Second-Order Three-Point Boundary Value Problem with a ParameterJian Liu0Hanying Feng1Xingfang Feng2Department of Mathematics, Shijiazhuang Mechanical Engineering College, Shijiazhuang, Hebei 050003, ChinaDepartment of Mathematics, Shijiazhuang Mechanical Engineering College, Shijiazhuang, Hebei 050003, ChinaDepartment of Mathematics, Shijiazhuang Mechanical Engineering College, Shijiazhuang, Hebei 050003, ChinaThis paper is concerned with the following second-order three-point boundary value problem u″t+β2ut+λqtft,ut=0, t∈0 , 1, u0=0, u(1)=δu(η), where β∈(0,π/2), δ>0, η∈(0,1), and λ is a positive parameter. First, Green’s function for the associated linear boundary value problem is constructed, and then some useful properties of Green’s function are obtained. Finally, existence, multiplicity, and nonexistence results for positive solutions are derived in terms of different values of λ by means of the fixed point index theory.http://dx.doi.org/10.1155/2014/603203 |
| spellingShingle | Jian Liu Hanying Feng Xingfang Feng Multiplicity of Positive Solutions for a Singular Second-Order Three-Point Boundary Value Problem with a Parameter Journal of Applied Mathematics |
| title | Multiplicity of Positive Solutions for a Singular Second-Order Three-Point Boundary Value Problem with a Parameter |
| title_full | Multiplicity of Positive Solutions for a Singular Second-Order Three-Point Boundary Value Problem with a Parameter |
| title_fullStr | Multiplicity of Positive Solutions for a Singular Second-Order Three-Point Boundary Value Problem with a Parameter |
| title_full_unstemmed | Multiplicity of Positive Solutions for a Singular Second-Order Three-Point Boundary Value Problem with a Parameter |
| title_short | Multiplicity of Positive Solutions for a Singular Second-Order Three-Point Boundary Value Problem with a Parameter |
| title_sort | multiplicity of positive solutions for a singular second order three point boundary value problem with a parameter |
| url | http://dx.doi.org/10.1155/2014/603203 |
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