Geodesic
Positive solutions for singular three-point boundary-value problems with sign changing nonlinearities depending on \(x'\)
Electronic journal of differential equations, Tome 2007 (2007)
Using a fixed point theorem in cones, this paper shows the existence of positive solutions for the singular three-point boundary-value problem

$\displaylines{ x''(t)+a(t)f(t,x(t),x'(t))=0,\quad 0 less than t less than 1,\cr x'(0)=0,\quad x(1)=\alpha x(\eta), }$

where $0 less than \alpha less than 1, 0 less than \eta less than 1$, and $f$ may change sign and may be singular at $x=0$ and $x'=0$.
Classification : 34B15, 34B10
Keywords: three-point boundary value problem, singularity, positive solutions, fixed point theorem 
@article{EJDE_2007__2007__a101,
     author = {Chen,  Yun and Yan,  Baoqiang and Zhang,  Lili},
     title = {Positive solutions for singular three-point boundary-value problems with sign changing nonlinearities depending on \(x'\)},
     journal = {Electronic journal of differential equations},
     year = {2007},
     volume = {2007},
     zbl = {1141.34309},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2007__2007__a101/}
}
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%J Electronic journal of differential equations
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Chen,  Yun; Yan,  Baoqiang; Zhang,  Lili. Positive solutions for singular three-point boundary-value problems with sign changing nonlinearities depending on \(x'\). Electronic journal of differential equations, Tome 2007 (2007). http://geodesic.mathdoc.fr/item/EJDE_2007__2007__a101/