Three positive solutions for multipoint one-dimensional p-Laplacian boundary value problems with dependence on the first order derivative
By applying a fixed point theorem due to Avery and Peterson, we study the existence of at least three positive solutions for the one-dimensional p-Laplacian differential equation, (phi(p) (u'(t)))' + q (t) f (t, u (t), u'(t)) = 0, t is an element of (0, 1), subject to the following multipoint boundary condition, u'(0)=Sigma(n)(i=1)a(i)u'(xi(i)), u(1)=Sigma(n)(i=1)beta(i)u(xi(i)), where phi(p)(s) = vertical bar s vertical bar(p-2)s with p > 1. The interesting point is the nonlinear term f is involved with the first-order derivative explicitly. (c) 2006 Elsevier Ltd. All rights reserved.
positive solutions p-laplacian fixed point theorem multipoint boundary value problem