Triple symmetric positive solutions for multipoint boundary-value problem with one-dimensional p-Laplacian
in this paper, we consider the multipoint boundary value problem for one-dimensional p-Laplacian (phi(p) (u'(t)))' + q (t) f (t, u(t), u'(t)) = 0, t is an element of (0, 1), subject to the boundary conditions: n n u(0) - (n)Sigma(i=1) mu(i) u'(xi(i)) = 0, u(1) + (n)Sigma(i=1) mu(i) u' (eta(i)) = 0, where phi(p) (s) = |s|(p-2)s, p > 1, mu(i) > 0, 0 < xi(1) < xi(2) < ... < xi(n) < 1/2, xi(i) + eta(i) = 1, i = 1, 2, ... , n. Applying the fixed point theorem due to Avery and Peterson, we study the existence of at least three symmetric positive solutions to the above boundary value problem. The interesting point is that the nonlinear term f contains the first-order derivative explicitly and the boundary condition is of Sturm-Liouville type. (C) 2007 Elsevier Ltd. All rights reserved.
symmetric positive solution one-dimensional p-laplacian multipoint boundary value problem avery-peterson's fixed point theorem