scholarly journals On the uniqueness of the positive solution for a second-order integral boundary value problem with switched nonlinearity

2011 ◽  
Vol 24 (12) ◽  
pp. 2201-2205 ◽  
Author(s):  
Haitao Li ◽  
Yansheng Liu
Keyword(s):  
Boundary Value Problem ◽  
Positive Solution ◽  
Boundary Value ◽  
Second Order ◽  
Integral Boundary ◽  
Integral Boundary Value Problem

scholarly journals Positive Solution of Fourth-Order Integral Boundary Value Problem with Two Parameters

2011 ◽  
Vol 2011 ◽  
pp. 1-19 ◽  
Author(s):  
Guoqing Chai
Keyword(s):  
Boundary Value Problem ◽  
Positive Solution ◽  
Fourth Order ◽  
Boundary Value ◽  
Index Theorem ◽  
Integral Boundary ◽  
Integral Boundary Value Problem ◽  
Operator Spectrum ◽  
Fixed Point Index Theorem ◽  
Two Parameters

The author investigates the fourth-order integral boundary value problem with two parametersu(4)(t)+βu′′(t)-αu(t)=f(t,u),t∈(0,1),  u(0)=u(1)=0,  u′′(0)=∫01u(s)ϕ1(s)ds,u′′(1)=∫01u(s)ϕ2(s)ds, where nonlinear term functionfis allowed to change sign. Applying the fixed point index theorem on cone together with the operator spectrum theorem, some results on the existence of positive solution are obtained.

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