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 paper considers the eigenvalue problem for the Sturm-Liouville problem including p-Laplacian {(|u' |p2 u') + (λ + r(x)) |u|p−2u = 0, x ∈ (0, πp), u(0)=u(πp) =0, where 1 < p < ∞, λ < p − 1, πp is the generalized π given by πp = 2π/ (p sin(π/p)) and r ∈ C[0, πp]. 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
Pages (from-to)383-399
Number of pages17
JournalDifferential and Integral Equations
Volume34
Issue number7-8
Publication statusPublished - 2021 Jul

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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