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).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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__a201,
     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},
     publisher = {mathdoc},
     volume = {2007},
     year = {2007},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2007__2007__a201/}
}
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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__a201/