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

2025/08/17 by Shalmali Bandyopadhyay, Bandyopadhyay, Shalmali, Fatma Ayça Çetinkaya +3
Physics and Astronomy · Computer Science · Mathematics · #Quantum chaos and dynamical systems #Nonlinear Dynamics and Pattern Formation #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2508.12369

Abstract

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.

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