Geodesic
Positive solutions to generalized second-order three-point integral boundary-value problems
Electronic journal of differential equations, Tome 2011 (2011)
In this article, by using Krasnoselskii's fixed point theorem, we obtain single and multiple positive solutions to the nonlinear second-order three-point integral boundary value problem

$\displaylines{ u''(t)+a(t)f(u(t))=0,\quad 0, \cr u(0)=\beta\int_0^{\eta}u(s)ds,\quad \alpha\int_0^{\eta}u(s)ds=u(T), }$

where $0\eta$ are given constants. As an application, we give some examples that illustrate our results.
Classification : 34B15, 34K10
Keywords: positive solution, three-point boundary value problem, fixed point theorem, cone 
@article{EJDE_2011__2011__a55,
     author = {Chasreechai,  Saowaluk and Tariboon,  Jessada},
     title = {Positive solutions to generalized second-order three-point integral boundary-value problems},
     journal = {Electronic journal of differential equations},
     year = {2011},
     volume = {2011},
     zbl = {1211.34025},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2011__2011__a55/}
}
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Chasreechai,  Saowaluk; Tariboon,  Jessada. Positive solutions to generalized second-order three-point integral boundary-value problems. Electronic journal of differential equations, Tome 2011 (2011). http://geodesic.mathdoc.fr/item/EJDE_2011__2011__a55/