Multiple Positive Solutions of Third-Order BVP with Advanced Arguments and Stieltjes Integral Conditions
We consider the following third-order boundary value problem with advanced arguments and Stieltjes integral boundary conditions: u′′′t+ft,uαt=0, t∈0,1, u0=γuη1+λ1u and u′′0=0, u1=βuη2+λ2u, where 0<η1<η2<1, 0≤γ,β≤1, α:[0,1]→[0,1] is continuous, α(t)≥t for t∈[0,1], and α(t)≤η2 for t∈[η1,η2...
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| Format: | Article |
| Language: | English |
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Wiley
2016-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2016/3805804 |
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| _version_ | 1832551586736373760 |
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| author | Jian Chang Jian-Ping Sun Ya-Hong Zhao |
| author_facet | Jian Chang Jian-Ping Sun Ya-Hong Zhao |
| author_sort | Jian Chang |
| collection | DOAJ |
| description | We consider the following third-order boundary value problem with advanced arguments and Stieltjes integral boundary conditions: u′′′t+ft,uαt=0, t∈0,1, u0=γuη1+λ1u and u′′0=0, u1=βuη2+λ2u, where 0<η1<η2<1, 0≤γ,β≤1, α:[0,1]→[0,1] is continuous, α(t)≥t for t∈[0,1], and α(t)≤η2 for t∈[η1,η2]. Under some suitable conditions, by applying a fixed point theorem due to Avery and Peterson, we obtain the existence of multiple positive solutions to the above problem. An example is also included to illustrate the main results obtained. |
| format | Article |
| id | doaj-art-14e95c29bd48412790563e615804036f |
| institution | Kabale University |
| issn | 2314-8896 2314-8888 |
| language | English |
| publishDate | 2016-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-14e95c29bd48412790563e615804036f2025-02-03T06:01:05ZengWileyJournal of Function Spaces2314-88962314-88882016-01-01201610.1155/2016/38058043805804Multiple Positive Solutions of Third-Order BVP with Advanced Arguments and Stieltjes Integral ConditionsJian Chang0Jian-Ping Sun1Ya-Hong Zhao2Department of Applied Mathematics, Lanzhou University of Technology, Lanzhou 730050, ChinaDepartment of Applied Mathematics, Lanzhou University of Technology, Lanzhou 730050, ChinaDepartment of Applied Mathematics, Lanzhou University of Technology, Lanzhou 730050, ChinaWe consider the following third-order boundary value problem with advanced arguments and Stieltjes integral boundary conditions: u′′′t+ft,uαt=0, t∈0,1, u0=γuη1+λ1u and u′′0=0, u1=βuη2+λ2u, where 0<η1<η2<1, 0≤γ,β≤1, α:[0,1]→[0,1] is continuous, α(t)≥t for t∈[0,1], and α(t)≤η2 for t∈[η1,η2]. Under some suitable conditions, by applying a fixed point theorem due to Avery and Peterson, we obtain the existence of multiple positive solutions to the above problem. An example is also included to illustrate the main results obtained.http://dx.doi.org/10.1155/2016/3805804 |
| spellingShingle | Jian Chang Jian-Ping Sun Ya-Hong Zhao Multiple Positive Solutions of Third-Order BVP with Advanced Arguments and Stieltjes Integral Conditions Journal of Function Spaces |
| title | Multiple Positive Solutions of Third-Order BVP with Advanced Arguments and Stieltjes Integral Conditions |
| title_full | Multiple Positive Solutions of Third-Order BVP with Advanced Arguments and Stieltjes Integral Conditions |
| title_fullStr | Multiple Positive Solutions of Third-Order BVP with Advanced Arguments and Stieltjes Integral Conditions |
| title_full_unstemmed | Multiple Positive Solutions of Third-Order BVP with Advanced Arguments and Stieltjes Integral Conditions |
| title_short | Multiple Positive Solutions of Third-Order BVP with Advanced Arguments and Stieltjes Integral Conditions |
| title_sort | multiple positive solutions of third order bvp with advanced arguments and stieltjes integral conditions |
| url | http://dx.doi.org/10.1155/2016/3805804 |
| work_keys_str_mv | AT jianchang multiplepositivesolutionsofthirdorderbvpwithadvancedargumentsandstieltjesintegralconditions AT jianpingsun multiplepositivesolutionsofthirdorderbvpwithadvancedargumentsandstieltjesintegralconditions AT yahongzhao multiplepositivesolutionsofthirdorderbvpwithadvancedargumentsandstieltjesintegralconditions |