Geodesic
Existence of three solutions for a Kirchhoff-type boundary-value problem
Electronic journal of differential equations, Tome 2011 (2011)
In this note, we establish the existence of two intervals of positive real parameters

$\displaylines{ -K\big(\int_{a}^b |u'(x)|^2dx\big)u''=\lambda f(x,u),\cr u(a)=u(b)=0 }$

admits three weak solutions whose norms are uniformly bounded with respect to $\lambda$ belonging to one of the two intervals. Our main tool is a three critical point theorem by Bonanno.
Classification : 35J20, 35J25, 35J60
Keywords: Kirchhoff-type problem, multiple solutions, critical point 
@article{EJDE_2011__2011__a74,
     author = {Heidarkhani,  Shapour and Afrouzi,  Ghasem Alizadeh and O'Regan,  Donal},
     title = {Existence of three solutions for a {Kirchhoff-type} boundary-value problem},
     journal = {Electronic journal of differential equations},
     year = {2011},
     volume = {2011},
     zbl = {1234.34018},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2011__2011__a74/}
}
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Heidarkhani,  Shapour; Afrouzi,  Ghasem Alizadeh; O'Regan,  Donal. Existence of three solutions for a Kirchhoff-type boundary-value problem. Electronic journal of differential equations, Tome 2011 (2011). http://geodesic.mathdoc.fr/item/EJDE_2011__2011__a74/