Lyapunov-type inequalities for a Sturm-Liouville problem of the one-dimensional p-Laplacian

Shingo Takeuchi; Kohtaro Watanabe

Lyapunov-type inequalities for a Sturm-Liouville problem of the one-dimensional p-Laplacian

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Abstract

This article considers the eigenvalue problem for the Sturm-Liouville problem including p-Laplacian (Formula Presented), where 1 < p < ∞, π_p is the generalized π given by π_p = 2π/ (p sin(π/p)), r ∈ C[0, π_p] and λ < p − 1. Sharp Lyapunov-type inequalities, which are necessary conditions for the existence of nontrivial solutions of the above problem are presented. Results are obtained through the analysis of variational problem related to a sharp Sobolev embedding and generalized trigonometric and hyperbolic functions.

Original language	English
Journal	Unknown Journal
Publication status	Published - 2020 Oct 4

Keywords

Generalized hyperbolic functions
Generalized trigonometric functions
Lyapunov-type inequality
p-Laplacian
Sharp Sobolev inequality

ASJC Scopus subject areas

General

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title = "Lyapunov-type inequalities for a Sturm-Liouville problem of the one-dimensional p-Laplacian",

abstract = "This article considers the eigenvalue problem for the Sturm-Liouville problem including p-Laplacian (Formula Presented), where 1 < p < ∞, πp is the generalized π given by πp = 2π/ (p sin(π/p)), r ∈ C[0, πp] and λ < p − 1. Sharp Lyapunov-type inequalities, which are necessary conditions for the existence of nontrivial solutions of the above problem are presented. Results are obtained through the analysis of variational problem related to a sharp Sobolev embedding and generalized trigonometric and hyperbolic functions.",

keywords = "Generalized hyperbolic functions, Generalized trigonometric functions, Lyapunov-type inequality, p-Laplacian, Sharp Sobolev inequality",

author = "Shingo Takeuchi and Kohtaro Watanabe",

year = "2020",

month = oct,

day = "4",

language = "English",

journal = "Unknown Journal",

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T1 - Lyapunov-type inequalities for a Sturm-Liouville problem of the one-dimensional p-Laplacian

AU - Takeuchi, Shingo

AU - Watanabe, Kohtaro

PY - 2020/10/4

Y1 - 2020/10/4

N2 - This article considers the eigenvalue problem for the Sturm-Liouville problem including p-Laplacian (Formula Presented), where 1 < p < ∞, πp is the generalized π given by πp = 2π/ (p sin(π/p)), r ∈ C[0, πp] and λ < p − 1. Sharp Lyapunov-type inequalities, which are necessary conditions for the existence of nontrivial solutions of the above problem are presented. Results are obtained through the analysis of variational problem related to a sharp Sobolev embedding and generalized trigonometric and hyperbolic functions.

AB - This article considers the eigenvalue problem for the Sturm-Liouville problem including p-Laplacian (Formula Presented), where 1 < p < ∞, πp is the generalized π given by πp = 2π/ (p sin(π/p)), r ∈ C[0, πp] and λ < p − 1. Sharp Lyapunov-type inequalities, which are necessary conditions for the existence of nontrivial solutions of the above problem are presented. Results are obtained through the analysis of variational problem related to a sharp Sobolev embedding and generalized trigonometric and hyperbolic functions.

KW - Generalized hyperbolic functions

KW - Generalized trigonometric functions

KW - Lyapunov-type inequality

KW - p-Laplacian

KW - Sharp Sobolev inequality

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