Geodesic
Existence of three solutions for a Kirchhoff-type boundary-value problem
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 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},
     publisher = {mathdoc},
     volume = {2011},
     year = {2011},
     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/