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.

引用

页码：3070 / 3083

页数：14

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