Sharp conditions for the existence of sign-changing solutions to equations involving the one-dimensional p-Laplacian

被引：22
|
作者：
Naito, Yuki [1 ]
Tanaka, Satoshi [2 ]
机构：
[1] Kobe Univ, Dept Appl Math, Grad Sch Engn, Nada Ku, Kobe, Hyogo 6578501, Japan
[2] Okayama Univ Sci, Dept Appl Math, Fac Sci, Okayama 7000005, Japan
来源：
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2008年 / 69卷 / 09期
关键词：
Two-point boundary value problems; One-dimensional p-Laplacian; Half-linear differential equations; Shooting method;
D O I：
10.1016/j.na.2007.09.002
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We consider the boundary value problem involving the one-dimensional p-Laplacian (vertical bar u'vertical bar(p-2)u')' + a(x) f (u) = 0. o < x <1. u(0) = u(1) = 0. where p > 1. We establish sharp conditions for the existence of solutions with prescribed numbers of zeros in terms of the ratio f (s)/s(p-1) at infinity and zero. Our argument is based on the shooting method together with the qualitative theory for half-linear differential equations. (C) 2007 Elsevier Ltd. All rights reserved.
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页码：3070 / 3083
页数：14
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