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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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
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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| Summary: | 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. |
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| ISSN: | 1026-0226 1607-887X |