TY - JOUR

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

AU - Takeuchi, Shingo

AU - Watanabe, Kohtaro

N1 - Funding Information:
AMS Subject Classifications: 34L10, 46E35. Accepted for publication: May 2021. 1This work is partially supported by the Grant-in-Aid for Scientific Research (C) (No. 17K05336) from Japan Society for the Promotion of Science. 2This work is partially supported by the Grant-in-Aid for Scientific Research (C) (No. 18K03387) from Japan Society for the Promotion of Science.
Publisher Copyright:
© 2021 Differential and Integral Equations.

PY - 2021/7

Y1 - 2021/7

N2 - This paper considers the eigenvalue problem for the Sturm-Liouville problem including p-Laplacian {(|u' |p−2 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.

AB - This paper considers the eigenvalue problem for the Sturm-Liouville problem including p-Laplacian {(|u' |p−2 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.

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M3 - Article

AN - SCOPUS:85108872461

VL - 34

SP - 383

EP - 399

JO - Differential and Integral Equations

JF - Differential and Integral Equations

SN - 0893-4983

IS - 7-8

ER -