A necessary and sufficient condition of positive solutions for nonlinear singular differential systems with four-point boundary conditions
In this paper, we concert with the existence of positive solution for the following nonlinear singular differential system with four-point boundary conditions{-x''=f(t,y),ax(0)-ßx'(0)=dx(1)+?x'(1)=0,-y''=g(t,x),y(0)=ay(?1),y(1)=by(?2),where 0<?1<?2<...
| Main Authors: | , |
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| Format: | Journal Article |
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Elsevier Inc.
2010
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| Online Access: | http://hdl.handle.net/20.500.11937/30685 |
| _version_ | 1848753159176978432 |
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| author | Zhang, Xinguang Liu, L. |
| author_facet | Zhang, Xinguang Liu, L. |
| author_sort | Zhang, Xinguang |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | In this paper, we concert with the existence of positive solution for the following nonlinear singular differential system with four-point boundary conditions{-x''=f(t,y),ax(0)-ßx'(0)=dx(1)+?x'(1)=0,-y''=g(t,x),y(0)=ay(?1),y(1)=by(?2),where 0<?1<?2<1,a,ß,d,?,a,b are nonnegative constants such that ?=ß?+a?+ad>0. By structuring upper and lower solution and using Schauder fixed point theorem, a necessary and sufficient condition for the existence of positive solutions is established. An example is worked out to illustrate our main result. |
| first_indexed | 2025-11-14T08:20:05Z |
| format | Journal Article |
| id | curtin-20.500.11937-30685 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T08:20:05Z |
| publishDate | 2010 |
| publisher | Elsevier Inc. |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-306852017-09-13T12:23:25Z A necessary and sufficient condition of positive solutions for nonlinear singular differential systems with four-point boundary conditions Zhang, Xinguang Liu, L. Schauder fixed point theorem Necessary and sufficient condition Differential systems Positive solutions In this paper, we concert with the existence of positive solution for the following nonlinear singular differential system with four-point boundary conditions{-x''=f(t,y),ax(0)-ßx'(0)=dx(1)+?x'(1)=0,-y''=g(t,x),y(0)=ay(?1),y(1)=by(?2),where 0<?1<?2<1,a,ß,d,?,a,b are nonnegative constants such that ?=ß?+a?+ad>0. By structuring upper and lower solution and using Schauder fixed point theorem, a necessary and sufficient condition for the existence of positive solutions is established. An example is worked out to illustrate our main result. 2010 Journal Article http://hdl.handle.net/20.500.11937/30685 10.1016/j.amc.2009.10.044 Elsevier Inc. restricted |
| spellingShingle | Schauder fixed point theorem Necessary and sufficient condition Differential systems Positive solutions Zhang, Xinguang Liu, L. A necessary and sufficient condition of positive solutions for nonlinear singular differential systems with four-point boundary conditions |
| title | A necessary and sufficient condition of positive solutions for nonlinear singular differential systems with four-point boundary conditions |
| title_full | A necessary and sufficient condition of positive solutions for nonlinear singular differential systems with four-point boundary conditions |
| title_fullStr | A necessary and sufficient condition of positive solutions for nonlinear singular differential systems with four-point boundary conditions |
| title_full_unstemmed | A necessary and sufficient condition of positive solutions for nonlinear singular differential systems with four-point boundary conditions |
| title_short | A necessary and sufficient condition of positive solutions for nonlinear singular differential systems with four-point boundary conditions |
| title_sort | necessary and sufficient condition of positive solutions for nonlinear singular differential systems with four-point boundary conditions |
| topic | Schauder fixed point theorem Necessary and sufficient condition Differential systems Positive solutions |
| url | http://hdl.handle.net/20.500.11937/30685 |