Green’s Function and Positive Solutions for a Second-Order Singular Boundary Value Problem with Integral Boundary Conditions and a Delayed Argument
This paper investigates the expression and properties of Green’s function for a second-order singular boundary value problem with integral boundary conditions and delayed argument -x′′t-atx′t+btxt=ωtft, xαt, t∈0, 1; x′0=0, x1-∫01htxtdt=0, where a∈0, 1, 0, +∞, b∈C0, 1, 0, +∞ and, ω may be singular...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/393187 |
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| author | Xuemei Zhang Meiqiang Feng |
| author_facet | Xuemei Zhang Meiqiang Feng |
| author_sort | Xuemei Zhang |
| collection | DOAJ |
| description | This paper investigates the expression and properties of Green’s function for a second-order singular boundary value problem with integral boundary conditions and delayed argument -x′′t-atx′t+btxt=ωtft, xαt, t∈0, 1; x′0=0, x1-∫01htxtdt=0, where a∈0, 1, 0, +∞, b∈C0, 1, 0, +∞ and, ω may be singular at t=0 or/and at t=1. Furthermore, several new and more general results are obtained for the existence of positive solutions for the above problem by using Krasnosel’skii’s fixed point theorem. We discuss our problems with a delayed argument, which may concern optimization issues of some technical problems. Moreover, the approach to express the integral equation of the above problem is different from earlier approaches. Our results cover a second-order boundary value problem without deviating arguments and are compared with some recent results. |
| format | Article |
| id | doaj-art-d56edaed8a0148cfb38a7f648ffc1476 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-d56edaed8a0148cfb38a7f648ffc14762025-02-03T05:59:49ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/393187393187Green’s Function and Positive Solutions for a Second-Order Singular Boundary Value Problem with Integral Boundary Conditions and a Delayed ArgumentXuemei Zhang0Meiqiang Feng1Department of Mathematics and Physics, North China Electric Power University, Beijing 102206, ChinaSchool of Applied Science, Beijing Information Science & Technology University, Beijing 100192, ChinaThis paper investigates the expression and properties of Green’s function for a second-order singular boundary value problem with integral boundary conditions and delayed argument -x′′t-atx′t+btxt=ωtft, xαt, t∈0, 1; x′0=0, x1-∫01htxtdt=0, where a∈0, 1, 0, +∞, b∈C0, 1, 0, +∞ and, ω may be singular at t=0 or/and at t=1. Furthermore, several new and more general results are obtained for the existence of positive solutions for the above problem by using Krasnosel’skii’s fixed point theorem. We discuss our problems with a delayed argument, which may concern optimization issues of some technical problems. Moreover, the approach to express the integral equation of the above problem is different from earlier approaches. Our results cover a second-order boundary value problem without deviating arguments and are compared with some recent results.http://dx.doi.org/10.1155/2014/393187 |
| spellingShingle | Xuemei Zhang Meiqiang Feng Green’s Function and Positive Solutions for a Second-Order Singular Boundary Value Problem with Integral Boundary Conditions and a Delayed Argument Abstract and Applied Analysis |
| title | Green’s Function and Positive Solutions for a Second-Order Singular Boundary Value Problem with Integral Boundary Conditions and a Delayed Argument |
| title_full | Green’s Function and Positive Solutions for a Second-Order Singular Boundary Value Problem with Integral Boundary Conditions and a Delayed Argument |
| title_fullStr | Green’s Function and Positive Solutions for a Second-Order Singular Boundary Value Problem with Integral Boundary Conditions and a Delayed Argument |
| title_full_unstemmed | Green’s Function and Positive Solutions for a Second-Order Singular Boundary Value Problem with Integral Boundary Conditions and a Delayed Argument |
| title_short | Green’s Function and Positive Solutions for a Second-Order Singular Boundary Value Problem with Integral Boundary Conditions and a Delayed Argument |
| title_sort | green s function and positive solutions for a second order singular boundary value problem with integral boundary conditions and a delayed argument |
| url | http://dx.doi.org/10.1155/2014/393187 |
| work_keys_str_mv | AT xuemeizhang greensfunctionandpositivesolutionsforasecondordersingularboundaryvalueproblemwithintegralboundaryconditionsandadelayedargument AT meiqiangfeng greensfunctionandpositivesolutionsforasecondordersingularboundaryvalueproblemwithintegralboundaryconditionsandadelayedargument |