Bulletin of the Belgian Mathematical Society - Simon Stevin

Half-linear Sturm-Liouville problem with weights

Pavel Drábek and Komil Kuliev

Full-text: Open access

Abstract

We prove a necessary and sufficient conditions for discreteness of the set of all eigenvalues (with the usual Sturm--Liouville properties) of half--linear eigenvalue problem with locally integrable weights. Our conditions appear to be equivalent to the compact embedding of certain weighted Sobolev and Lebesgue spaces. Every eigenvalue allows the variational characterization of Ljusternik--Schnirelmann type.

Article information

Source
Bull. Belg. Math. Soc. Simon Stevin, Volume 19, Number 1 (2012), 107-119.

Dates
First available in Project Euclid: 7 March 2012

Permanent link to this document
https://projecteuclid.org/euclid.bbms/1331153412

Mathematical Reviews number (MathSciNet)
MR2952799

Zentralblatt MATH identifier
1252.34034

Subjects
Primary: 34L30: Nonlinear ordinary differential operators 34B24: Sturm-Liouville theory [See also 34Lxx]
Secondary: 34B40: Boundary value problems on infinite intervals 35J92: Quasilinear elliptic equations with p-Laplacian

Keywords
Hardy inequality weighted spaces Sturm-Liouville problem variational eigenvalues oscillatory theory

Citation

Drábek, Pavel; Kuliev, Komil. Half-linear Sturm-Liouville problem with weights. Bull. Belg. Math. Soc. Simon Stevin 19 (2012), no. 1, 107--119. https://projecteuclid.org/euclid.bbms/1331153412


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