Existence of multiple positive solutions for one-dimensional p-Laplacian

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:315

Article

Wang, YY ; Hou, CM

关键词: multiple positive solutions;    boundary value problems;    one-dimensional p-Laplacian;   

DOI  :  10.1016/j.jmaa.2005.09.085

来源: Elsevier

【 摘 要 】

In this paper we consider the multipoint boundary value problem for one-dimensional p-Laplacian (phi(p) (u'))' + f (t, U) = 0, t is an element of (0, 1), subject to the boundary value conditions: phi(rho) (U'(0)) = Sigma(i=1) a(i)phi(p)(u'(xi(i))), u(1)=Sigma(i=1)b(i)u(xi(i)), where phi(p)(s) = vertical bar s vertical bar(p-2)s, p > 1, xi(i) is an element of (0, 1) with 0 < xi(1) < xi(2) < (...) < xi(n-2) < 1, and a(i), b(i) satisfy a(i), b(i) is an element of [0, infinity], 0 < Sigma(i=1)(n-2) a(i) < 1 and Sigma(i=1)(n-2) b(i) < 1. Using a fixed point theorem for operators on a cone, we provide sufficient conditions for the existence of multiple (at least three) positive solutions to the above boundary value problem. (c) 2005 Elsevier Inc. All rights reserved.

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