Geodesic
Multiple positive solutions for fourth-order three-point \(p\)-Laplacian boundary-value problems
Electronic journal of differential equations, Tome 2007 (2007)
In this paper, we study the three-point boundary-value problem for a fourth-order one-dimensional

$ \big(\phi_p(u''(t))\big)''+ a(t)f\big(u(t)\big)=0, \quad t\in (0,1), $

subject to the nonlinear boundary conditions:

$\displaylines{ u(0)=\xi u(1),\quad u'(1)=\eta u'(0),\cr (\phi _{p}(u''(0))' =\alpha _{1}(\phi _{p}(u''(\delta))', \quad u''(1)=\sqrt[p-1]{\beta _{1}}u''(\delta), }$

where $\phi_{p}(s)=|s|^{p-2}s, p>1$. Using the five functional fixed point theorem due to Avery, we obtain sufficient conditions for the existence of at least three positive solutions.
Classification : 34B10, 34B15, 34B18
Keywords: fourth-order boundary-value problem, one-dimensional p-Laplacian, five functional fixed point theorem, positive solution 
@article{EJDE_2007__2007__a126,
     author = {Feng,  Hanying and Feng,  Meiqiang and Jiang,  Ming and Ge,  Weigao},
     title = {Multiple positive solutions for fourth-order three-point {\(p\)-Laplacian} boundary-value problems},
     journal = {Electronic journal of differential equations},
     year = {2007},
     volume = {2007},
     zbl = {1117.34010},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2007__2007__a126/}
}
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AU  - Feng,  Meiqiang
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AU  - Ge,  Weigao
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JO  - Electronic journal of differential equations
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%A Jiang,  Ming
%A Ge,  Weigao
%T Multiple positive solutions for fourth-order three-point \(p\)-Laplacian boundary-value problems
%J Electronic journal of differential equations
%D 2007
%V 2007
%U http://geodesic.mathdoc.fr/item/EJDE_2007__2007__a126/
%G en
%F EJDE_2007__2007__a126
Feng,  Hanying; Feng,  Meiqiang; Jiang,  Ming; Ge,  Weigao. Multiple positive solutions for fourth-order three-point \(p\)-Laplacian boundary-value problems. Electronic journal of differential equations, Tome 2007 (2007). http://geodesic.mathdoc.fr/item/EJDE_2007__2007__a126/