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

Shingo Takeuchi, Kohtaro Watanabe

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish
JournalUnknown Journal
Publication statusPublished - 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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