Electron. J. Diff. Equ., Vol. 2011 (2011), No. 75, pp. 1-10.

Three positive solutions for m-point boundary-value problems with one-dimensional p-Laplacian

Donglong Bai, Hanying Feng

Abstract:
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.

Submitted April 5, 2011. Published June 16, 2011.
Math Subject Classifications: 34B10, 34B15, 34B18.
Key Words: Multipoint boundary value problem; positive solution; Avery-Peterson fixed point theorem; one-dimensional p-Laplacian.

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Donglong Bai
Department of Mathematics
Shijiazhuang Mechanical Engineering College
Shijiazhuang 050003, Hebei, China
email: baidonglong@yeal.net
Hanying Feng
Department of Mathematics
Shijiazhuang Mechanical Engineering College
Shijiazhuang 050003, Hebei, China
email: fhanying@yahoo.com.cn

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