Geodesic
Positive solutions to a second-order multi-point boundary-value problem
Electronic journal of differential equations, Tome 2000 (2000)
We prove the existence of positive solutions to the boundary-value problem $ u''+\lambda a(t)f(u,u')=0 u(0)=0,\quad u(1)=\sum^{m-2}_{i=1} a_i u(\xi_i) $ , where $a$ is a continuous function that may change sign on [0,1], $f$ is a continuous function with $f(0,0)>0$, and $\lambda$ is a samll positive constant. For finding solutions we use the Leray-Schauder fixed point theorem.
Classification : 34B10
Keywords: multi-point boundary value problem, positive solution, fixed point theorem 
@article{EJDE_2000__2000__a171,
     author = {Cao,  Daomin and Ma,  Ruyun},
     title = {Positive solutions to a second-order multi-point boundary-value problem},
     journal = {Electronic journal of differential equations},
     year = {2000},
     volume = {2000},
     zbl = {0964.34022},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2000__2000__a171/}
}
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Cao,  Daomin; Ma,  Ruyun. Positive solutions to a second-order multi-point boundary-value problem. Electronic journal of differential equations, Tome 2000 (2000). http://geodesic.mathdoc.fr/item/EJDE_2000__2000__a171/