Electronic Journal of Differential Equations,
Vol. 2011 (2011), No. 75, pp. 1-10.
Title: Three positive solutions for m-point boundary-value problems
with one-dimensional p-Laplacian
Authors: Donglong Bai (Shijiazhuang Mechanical Engineering College, China)
Hanying Feng (Shijiazhuang Mechanical Engineering College, China)
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.