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

Yuki Naito; Satoshi Tanaka

doi:10.1016/j.na.2007.09.002

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

Yuki Naito, Satoshi Tanaka

Research output: Contribution to journal › Article › peer-review

4 Citations (Scopus)

Abstract

We consider the boundary value problem involving the one-dimensional p-Laplacian (| u^′ |^{p - 2} u^′)^′ + a (x) f (u) = 0, 0 < 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.

Original language	English
Pages (from-to)	3070-3083
Number of pages	14
Journal	Nonlinear Analysis, Theory, Methods and Applications
Volume	69
Issue number	9
DOIs	https://doi.org/10.1016/j.na.2007.09.002
Publication status	Published - 2008 Nov 1
Externally published	Yes

Keywords

Half-linear differential equations
One-dimensional p-Laplacian
Shooting method
Two-point boundary value problems

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.1016/j.na.2007.09.002

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

abstract = "We consider the boundary value problem involving the one-dimensional p-Laplacian (| u′ |p - 2 u′)′ + a (x) f (u) = 0, 0 < 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) / sp - 1 at infinity and zero. Our argument is based on the shooting method together with the qualitative theory for half-linear differential equations.",

keywords = "Half-linear differential equations, One-dimensional p-Laplacian, Shooting method, Two-point boundary value problems",

author = "Yuki Naito and Satoshi Tanaka",

year = "2008",

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T1 - Sharp conditions for the existence of sign-changing solutions to equations involving the one-dimensional p-Laplacian

AU - Naito, Yuki

AU - Tanaka, Satoshi

PY - 2008/11/1

Y1 - 2008/11/1

N2 - We consider the boundary value problem involving the one-dimensional p-Laplacian (| u′ |p - 2 u′)′ + a (x) f (u) = 0, 0 < 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) / sp - 1 at infinity and zero. Our argument is based on the shooting method together with the qualitative theory for half-linear differential equations.

AB - We consider the boundary value problem involving the one-dimensional p-Laplacian (| u′ |p - 2 u′)′ + a (x) f (u) = 0, 0 < 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) / sp - 1 at infinity and zero. Our argument is based on the shooting method together with the qualitative theory for half-linear differential equations.

KW - Half-linear differential equations

KW - One-dimensional p-Laplacian

KW - Shooting method

KW - Two-point boundary value problems

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DO - 10.1016/j.na.2007.09.002

M3 - Article

AN - SCOPUS:50349090609

SN - 0362-546X

VL - 69

SP - 3070

EP - 3083

JO - Nonlinear Analysis, Theory, Methods and Applications

JF - Nonlinear Analysis, Theory, Methods and Applications

IS - 9

ER -

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

Abstract

Keywords

ASJC Scopus subject areas

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