Geodesic
Positive solutions for an m-point boundary-value problem
Electronic journal of differential equations, Tome 2008 (2008)
In this paper, we obtain sufficient conditions for the existence of a positive solution, and infinitely many positive solutions, of the m-point boundary-value problem

$\displaylines{ x''(t) = f(t, x(t)), \quad 0 t 1, \cr x'(0) = 0, \quad x(1)=\sum_{i=1}^{m-2}\alpha _{i}x(\eta _{i})\,. }$

Our main tools are the Guo-Krasnoselskii's fixed point theorem and the monotone iterative technique. We also show that the set of positive solutions is compact.
Classification : 34B07, 34B10, 34B18, 34B27
Keywords: multi-point boundary, positive solution, guo-Krasnoselskii fixed point theorem 
@article{EJDE_2008__2008__a81,
     author = {Truong,  Le Xuan and Ngoc,  Le Thi Phuong and Long,  Nguyen Thanh},
     title = {Positive solutions for an m-point boundary-value problem},
     journal = {Electronic journal of differential equations},
     year = {2008},
     volume = {2008},
     zbl = {1171.34014},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2008__2008__a81/}
}
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Truong,  Le Xuan; Ngoc,  Le Thi Phuong; Long,  Nguyen Thanh. Positive solutions for an m-point boundary-value problem. Electronic journal of differential equations, Tome 2008 (2008). http://geodesic.mathdoc.fr/item/EJDE_2008__2008__a81/