Global Structure of Positive Solutions for a Singular Fourth-Order Integral Boundary Value Problem
We consider fourth-order boundary value problems u′′′′(t)=λh(t)f(u(t)), 0<t<1, u(0)=∫01u(s)dα(s), u′(0)=u(1)=u′(1)=0, where ∫01u(s)dα(s) is a Stieltjes integral with α(t) being nondecreasing and α(t) being not a constant on [0,1]; h(t) may be singular at t=0 and t=1, h∈C((0,1),[0,∞)) with...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2014/614376 |
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| author | Wenguo Shen Tao He |
| author_facet | Wenguo Shen Tao He |
| author_sort | Wenguo Shen |
| collection | DOAJ |
| description | We consider fourth-order boundary value problems u′′′′(t)=λh(t)f(u(t)), 0<t<1, u(0)=∫01u(s)dα(s), u′(0)=u(1)=u′(1)=0, where ∫01u(s)dα(s) is a Stieltjes integral with α(t) being nondecreasing and α(t) being not a constant on [0,1]; h(t) may be singular at t=0 and t=1, h∈C((0,1),[0,∞)) with h(t)≢0 on any subinterval of (0,1); f∈C([0,∞),[0,∞)) and f(s)>0 for all s>0, and f0=∞, f∞=0, f0=lims→0+f(s)/s, f∞=lims→+∞f(s)/s. We investigate the global structure of positive solutions by using global bifurcation techniques. |
| format | Article |
| id | doaj-art-725afab063404bdfae62e63fbcb7f6bb |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-725afab063404bdfae62e63fbcb7f6bb2025-02-03T01:10:17ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2014-01-01201410.1155/2014/614376614376Global Structure of Positive Solutions for a Singular Fourth-Order Integral Boundary Value ProblemWenguo Shen0Tao He1Department of Basic Courses, Lanzhou Institute of Technology, Lanzhou 730050, ChinaDepartment of Basic Courses, Lanzhou Institute of Technology, Lanzhou 730050, ChinaWe consider fourth-order boundary value problems u′′′′(t)=λh(t)f(u(t)), 0<t<1, u(0)=∫01u(s)dα(s), u′(0)=u(1)=u′(1)=0, where ∫01u(s)dα(s) is a Stieltjes integral with α(t) being nondecreasing and α(t) being not a constant on [0,1]; h(t) may be singular at t=0 and t=1, h∈C((0,1),[0,∞)) with h(t)≢0 on any subinterval of (0,1); f∈C([0,∞),[0,∞)) and f(s)>0 for all s>0, and f0=∞, f∞=0, f0=lims→0+f(s)/s, f∞=lims→+∞f(s)/s. We investigate the global structure of positive solutions by using global bifurcation techniques.http://dx.doi.org/10.1155/2014/614376 |
| spellingShingle | Wenguo Shen Tao He Global Structure of Positive Solutions for a Singular Fourth-Order Integral Boundary Value Problem Discrete Dynamics in Nature and Society |
| title | Global Structure of Positive Solutions for a Singular Fourth-Order Integral Boundary Value Problem |
| title_full | Global Structure of Positive Solutions for a Singular Fourth-Order Integral Boundary Value Problem |
| title_fullStr | Global Structure of Positive Solutions for a Singular Fourth-Order Integral Boundary Value Problem |
| title_full_unstemmed | Global Structure of Positive Solutions for a Singular Fourth-Order Integral Boundary Value Problem |
| title_short | Global Structure of Positive Solutions for a Singular Fourth-Order Integral Boundary Value Problem |
| title_sort | global structure of positive solutions for a singular fourth order integral boundary value problem |
| url | http://dx.doi.org/10.1155/2014/614376 |
| work_keys_str_mv | AT wenguoshen globalstructureofpositivesolutionsforasingularfourthorderintegralboundaryvalueproblem AT taohe globalstructureofpositivesolutionsforasingularfourthorderintegralboundaryvalueproblem |