Geodesic
Positive solutions to generalized second-order three-point integral boundary-value problems
Electronic Journal of Differential Equations, Tome 2011 (2011).

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

Summary: 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 
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     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},
     publisher = {mathdoc},
     volume = {2011},
     year = {2011},
     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/