Positive Solutions for a Class of Third-Order Three-Point Boundary Value Problem
We investigate the problem of existence of positive solutions for the nonlinear third-order three-point boundary value problem u‴(t)+λa(t)f(u(t))=0, 0<t<1, u(0)=u′(0)=0, u″(1)=∝u″(η), where λ is a positive parameter, ∝∈(0,1), η∈(0,1), f:(0,∞)→(0,∞), a:(0,1)→(0,∞) are continuous. Using a specia...
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2012/937670 |
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| _version_ | 1832555992795054080 |
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| author | Xiaojie Lin Zhengmin Fu |
| author_facet | Xiaojie Lin Zhengmin Fu |
| author_sort | Xiaojie Lin |
| collection | DOAJ |
| description | We investigate the problem of existence of positive solutions for the nonlinear third-order three-point boundary value problem
u‴(t)+λa(t)f(u(t))=0, 0<t<1, u(0)=u′(0)=0, u″(1)=∝u″(η), where λ is a positive parameter, ∝∈(0,1), η∈(0,1), f:(0,∞)→(0,∞), a:(0,1)→(0,∞) are continuous. Using a specially constructed cone, the fixed point index theorems and Leray-Schauder degree, this work shows the existence and multiplicities of positive solutions
for the nonlinear third-order boundary value problem. Some examples
are given to demonstrate the main results. |
| format | Article |
| id | doaj-art-635c5c83597743dfb361f9f699f6e54c |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-635c5c83597743dfb361f9f699f6e54c2025-02-03T05:46:43ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2012-01-01201210.1155/2012/937670937670Positive Solutions for a Class of Third-Order Three-Point Boundary Value ProblemXiaojie Lin0Zhengmin Fu1School of Mathematical Sciences, Jiangsu Normal University, Xuzhou, Jiangsu 221116, ChinaSchool of Mathematical Sciences, Jiangsu Normal University, Xuzhou, Jiangsu 221116, ChinaWe investigate the problem of existence of positive solutions for the nonlinear third-order three-point boundary value problem u‴(t)+λa(t)f(u(t))=0, 0<t<1, u(0)=u′(0)=0, u″(1)=∝u″(η), where λ is a positive parameter, ∝∈(0,1), η∈(0,1), f:(0,∞)→(0,∞), a:(0,1)→(0,∞) are continuous. Using a specially constructed cone, the fixed point index theorems and Leray-Schauder degree, this work shows the existence and multiplicities of positive solutions for the nonlinear third-order boundary value problem. Some examples are given to demonstrate the main results.http://dx.doi.org/10.1155/2012/937670 |
| spellingShingle | Xiaojie Lin Zhengmin Fu Positive Solutions for a Class of Third-Order Three-Point Boundary Value Problem Discrete Dynamics in Nature and Society |
| title | Positive Solutions for a Class of Third-Order Three-Point Boundary Value Problem |
| title_full | Positive Solutions for a Class of Third-Order Three-Point Boundary Value Problem |
| title_fullStr | Positive Solutions for a Class of Third-Order Three-Point Boundary Value Problem |
| title_full_unstemmed | Positive Solutions for a Class of Third-Order Three-Point Boundary Value Problem |
| title_short | Positive Solutions for a Class of Third-Order Three-Point Boundary Value Problem |
| title_sort | positive solutions for a class of third order three point boundary value problem |
| url | http://dx.doi.org/10.1155/2012/937670 |
| work_keys_str_mv | AT xiaojielin positivesolutionsforaclassofthirdorderthreepointboundaryvalueproblem AT zhengminfu positivesolutionsforaclassofthirdorderthreepointboundaryvalueproblem |