Prüfer Transformation and Spectral Analysis for a Sturm--Liouville-Type Equation

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Main Authors: Bandyopadhyay, Shalmali, Çetinkaya, F. Ayça, Cuchta, Tom
Format: Preprint
Published: 2025
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author Bandyopadhyay, Shalmali
Çetinkaya, F. Ayça
Cuchta, Tom
author_facet Bandyopadhyay, Shalmali
Çetinkaya, F. Ayça
Cuchta, Tom
contents We study a second-order differential equation involving a quasi-derivative, leading to a non-self-adjoint Sturm--Liouville-type problem with four coefficient functions. To analyze this equation, we develop a generalized Prüfer transformation that expresses solutions in terms of amplitude and phase variables. We further prove the monotonicity of eigenfunction zeros with respect to the spectral parameter and derive upper and lower bounds for the eigenvalues.
format Preprint
id arxiv_https___arxiv_org_abs_2508_12369
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Prüfer Transformation and Spectral Analysis for a Sturm--Liouville-Type Equation
Bandyopadhyay, Shalmali
Çetinkaya, F. Ayça
Cuchta, Tom
Classical Analysis and ODEs
Spectral Theory
34L15, 34B24, 34L05
We study a second-order differential equation involving a quasi-derivative, leading to a non-self-adjoint Sturm--Liouville-type problem with four coefficient functions. To analyze this equation, we develop a generalized Prüfer transformation that expresses solutions in terms of amplitude and phase variables. We further prove the monotonicity of eigenfunction zeros with respect to the spectral parameter and derive upper and lower bounds for the eigenvalues.
title Prüfer Transformation and Spectral Analysis for a Sturm--Liouville-Type Equation
topic Classical Analysis and ODEs
Spectral Theory
34L15, 34B24, 34L05
url https://arxiv.org/abs/2508.12369