Geodesic
Three positive solutions for \(m\)-point boundary-value problems with one-dimensional \(p\)-Laplacian
Electronic journal of differential equations, Tome 2011 (2011)
In this article, we study the multipoint boundary value problem for the one-dimensional p-Laplacian

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

subject to the boundary conditions

$ u(0)=\sum_{i=1}^{m-2} a_iu(\xi_i),\quad u'(1)=\beta u'(0). $

Using a fixed point theorem due to Avery and Peterson, we provide sufficient conditions for the existence of at least three positive solutions to the above boundary value problem. The interesting point is that the nonlinear term f involves the first derivative of the unknown function.
Classification : 34B10, 34B15, 34B18
Keywords: multipoint boundary value problem, positive solution, avery-Peterson fixed point theorem, one-dimensional p-Laplacian 
@article{EJDE_2011__2011__a0,
     author = {Bai,  Donglong and Feng,  Hanying},
     title = {Three positive solutions for \(m\)-point boundary-value problems with one-dimensional {\(p\)-Laplacian}},
     journal = {Electronic journal of differential equations},
     year = {2011},
     volume = {2011},
     zbl = {1230.34026},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2011__2011__a0/}
}
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Bai,  Donglong; Feng,  Hanying. Three positive solutions for \(m\)-point boundary-value problems with one-dimensional \(p\)-Laplacian. Electronic journal of differential equations, Tome 2011 (2011). http://geodesic.mathdoc.fr/item/EJDE_2011__2011__a0/