Titchmarsh's asymptotic formula for periodic eigenvalues and an extension to the \(p\)-Laplacian

DOI10.1016/J.JMAA.2007.06.017zbMath1145.34056OpenAlexW2093159151WikidataQ126247472 ScholiaQ126247472MaRDI QIDQ2473974

Michael S. P. Eastham, B. Malcolm Brown

Publication date: 5 March 2008

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2007.06.017

zbMATH Keywords

rotation number\(p\)-LaplacianPrüfer transformationperiodic eigenvalues

Mathematics Subject Classification ID

Sturm-Liouville theory (34B24) Asymptotic distribution of eigenvalues, asymptotic theory of eigenfunctions for ordinary differential operators (34L20) Linear boundary value problems for ordinary differential equations (34B05)

Related Items (3)

A survey on extremal problems of eigenvalues ⋮ On the asymptotic simplicity of periodic eigenvalues and Titchmarsh's formula ⋮ MAXIMIZATION OF EIGENVALUES OF ONE-DIMENSIONAL p-LAPLACIAN WITH INTEGRABLE POTENTIALS

Cites Work

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• Bounds for the positive eigenvalues of the \(p\)-Laplacian with decaying potential
• The rotation number for almost periodic potentials
• Some remarkable sine and cosine functions
• Eigenvalue and eigenfunction asymptotics for regular Sturm-Liouville problems
• Sturm-Liouville theory for the radial \(\Delta_p\)-operator
• Computing eigenvalues and Fučik-spectrum of the radially symmetric \(p\)-Laplacian
• Asymptotic approximations of eigenvalues and eigenfunctions for regular Sturm-Liouville problems
• Eine Umkehrung der Sturm-Liouvilleschen Eigenwertaufgabe. Bestimmung der Differentialgleichung durch die Eigenwerte
• THE ROTATION NUMBER APPROACH TO EIGENVALUES OF THE ONE-DIMENSIONAL p-LAPLACIAN WITH PERIODIC POTENTIALS
• Asymptotic estimates for the Sturm-Liouville spectrum
• Eigenvalue Asymptotics of Layered Media and Their Applications to the Inverse Problem
• Sturm--Liouville theory for the p-Laplacian
• On the Gaps in the Spectrum Associated with Hill's Equation
• Absence of high-energy spectral concentration for Dirac systems with divergent potentials
• On the Nature of the Spectrum of Singular Second Order Linear Differential Equations

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