Geodesic
Multiple positive solutions for nonlinear third-order three-point boundary-value problems
Electronic journal of differential equations, Tome 2007 (2007)
This paper concerns the nonlinear third-order three-point boundary-value problem

$\displaylines{ u'''(t)+h(t)f(u(t))=0, \quad t\in (0,1), \cr u(0)=u'(0)=0, \quad u'(1)=\alpha u'(\eta ), }$

where $0\eta 1$ and $1\alpha \frac 1\eta $. First, we establish the existence of at least three positive solutions by using the well-known Leggett-Williams fixed point theorem. And then, we prove the existence of at least $2m-1$ positive solutions for arbitrary positive integer $m$.
Classification : 34B10, 34B18
Keywords: third-order boundary value problem, positive solution, three-point boundary value problem, existence, cone, fixed point 
@article{EJDE_2007__2007__a61,
     author = {Guo,  Li-Jun and Sun,  Jian-Ping and Zhao,  Ya-Hong},
     title = {Multiple positive solutions for nonlinear third-order three-point boundary-value problems},
     journal = {Electronic journal of differential equations},
     year = {2007},
     volume = {2007},
     zbl = {1142.34317},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2007__2007__a61/}
}
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Guo,  Li-Jun; Sun,  Jian-Ping; Zhao,  Ya-Hong. Multiple positive solutions for nonlinear third-order three-point boundary-value problems. Electronic journal of differential equations, Tome 2007 (2007). http://geodesic.mathdoc.fr/item/EJDE_2007__2007__a61/