Geodesic
Positive solutions of a nonlinear three-point boundary-value problem
Electronic journal of differential equations, Tome 1999 (1999)
We study the existence of positive solutions to the boundary-value problem $ u''+a(t)f(u)=0,\quad t\in (0,1)u(0)=0,\quad\alpha u(\eta)=u(1)\,, $ where $0 less than \eta less than 1$ and $0 less than \alpha less than 1/\eta$. We show the existence of at least one positive solution if $f$ is either superlinear or sublinear by applying the fixed point theorem in cones.
Classification : 34B15
Keywords: second-order multi-point BVP, positive solution, cone, fixed point 
@article{EJDE_1999__1999__a36,
     author = {Ma,  Ruyun},
     title = {Positive solutions of a nonlinear three-point boundary-value problem},
     journal = {Electronic journal of differential equations},
     year = {1999},
     volume = {1999},
     zbl = {0926.34009},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_1999__1999__a36/}
}
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Ma,  Ruyun. Positive solutions of a nonlinear three-point boundary-value problem. Electronic journal of differential equations, Tome 1999 (1999). http://geodesic.mathdoc.fr/item/EJDE_1999__1999__a36/