Multiple positive solutions for some p-Laplacian boundary value problems

[摘要] This paper deals with the existence of multiple positive solutions for the one-dimensional p-Laplacian (phi(p)(x'(t)))' + q (t) f (t, x(t), x'(t)) = 0, t is an element of (0, 1), subject to one of the following boundary conditions: alphaphi(p)(x(0)) - betaphi(p)(x'(0)) = 0, gammaphi(p)(x(1)) + 8 deltaphi(p)(x'(l)) = 0, or x (0) - g(1) (x'(0)) = 0, x(1) + g(2) (x'(1)) = 0, where phi(p)(s) = \s\(p-2) s, p > 1. By means of a fixed point theorem due to Avery and Peterson, sufficient conditions are obtained that guarantee the existence of at least three positive solutions. The interesting point is the nonlinear term f is involved with the first-order derivative explicitly. (C) 2004 Elsevier Inc. All rights reserved.

[发布日期] 2004-12-15

[关键词] triple positive solutions;p-Laplacian;boundary value problem;fixed point theorem