Geodesic
Multiple positive solutions for fourth-order three-point $p$-Laplacian boundary-value problems
Electronic Journal of Differential Equations, Tome 2007 (2007).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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__a226,
     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},
     publisher = {mathdoc},
     volume = {2007},
     year = {2007},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2007__2007__a226/}
}
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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__a226/