Existence of Positive Solutions for Nonlinear Third-Order Boundary Value Problem
We are concerned with the existence of positive solutions for the nonlinear third-order three-point boundary value problem u′′′(t)+λg(t)f(u(t))=0, 0<t<1, u(0)=αu(η), u′(0)=u′′(1)=0, where 0<η<1, 0<α<1, λ is a positive parameter, g:(0,1)→[0,∞), and f:[0,∞)→[0,∞) is continuous. We...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2014-01-01
|
| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2014/951947 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1849398990031814656 |
|---|---|
| author | Tiaoxia Dun Pengyu Chen |
| author_facet | Tiaoxia Dun Pengyu Chen |
| author_sort | Tiaoxia Dun |
| collection | DOAJ |
| description | We are concerned with the existence of positive solutions for the nonlinear third-order three-point boundary value problem u′′′(t)+λg(t)f(u(t))=0, 0<t<1, u(0)=αu(η), u′(0)=u′′(1)=0, where 0<η<1, 0<α<1, λ is a positive parameter, g:(0,1)→[0,∞), and f:[0,∞)→[0,∞) is continuous. We construct Green’s function for the associated linear boundary value problem and obtain some useful properties of Green’s function. Finally, by using fixed-point index theorem in cones, we establish the existence results of positive solutions for the boundary value problem an example illustrates the application of the results obtained. |
| format | Article |
| id | doaj-art-a434bc7e438048d6958f62b4fc5f82bc |
| institution | Kabale University |
| issn | 2314-4629 2314-4785 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-a434bc7e438048d6958f62b4fc5f82bc2025-08-20T03:38:26ZengWileyJournal of Mathematics2314-46292314-47852014-01-01201410.1155/2014/951947951947Existence of Positive Solutions for Nonlinear Third-Order Boundary Value ProblemTiaoxia Dun0Pengyu Chen1Department of Mathematics, Northwest Normal University, Lanzhou 730070, ChinaDepartment of Mathematics, Northwest Normal University, Lanzhou 730070, ChinaWe are concerned with the existence of positive solutions for the nonlinear third-order three-point boundary value problem u′′′(t)+λg(t)f(u(t))=0, 0<t<1, u(0)=αu(η), u′(0)=u′′(1)=0, where 0<η<1, 0<α<1, λ is a positive parameter, g:(0,1)→[0,∞), and f:[0,∞)→[0,∞) is continuous. We construct Green’s function for the associated linear boundary value problem and obtain some useful properties of Green’s function. Finally, by using fixed-point index theorem in cones, we establish the existence results of positive solutions for the boundary value problem an example illustrates the application of the results obtained.http://dx.doi.org/10.1155/2014/951947 |
| spellingShingle | Tiaoxia Dun Pengyu Chen Existence of Positive Solutions for Nonlinear Third-Order Boundary Value Problem Journal of Mathematics |
| title | Existence of Positive Solutions for Nonlinear Third-Order Boundary Value Problem |
| title_full | Existence of Positive Solutions for Nonlinear Third-Order Boundary Value Problem |
| title_fullStr | Existence of Positive Solutions for Nonlinear Third-Order Boundary Value Problem |
| title_full_unstemmed | Existence of Positive Solutions for Nonlinear Third-Order Boundary Value Problem |
| title_short | Existence of Positive Solutions for Nonlinear Third-Order Boundary Value Problem |
| title_sort | existence of positive solutions for nonlinear third order boundary value problem |
| url | http://dx.doi.org/10.1155/2014/951947 |
| work_keys_str_mv | AT tiaoxiadun existenceofpositivesolutionsfornonlinearthirdorderboundaryvalueproblem AT pengyuchen existenceofpositivesolutionsfornonlinearthirdorderboundaryvalueproblem |