Galoisian approach for a Sturm-Liouville problem on the infinite\n interval

2010/09/06 by David Blázquez-Sanz, Blazquez-Sanz, David, Kazuyuki Yagasaki +1 · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #34B09 #34B24 #35B35 #81Q05 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum chaos and dynamical systems #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.1009.0979

openalex publication_date 2010/09/06 · openalex created_date 2022/10/03 · openalex updated_date 2026/07/28

Abstract

We study a Sturm-Liouville type eigenvalue problem for second-order\ndifferential equations on the infinite interval. Here the eigenfunctions are\nnonzero solutions exponentially decaying at infinity. We prove that at any\ndiscrete eigenvalue the differential equations are integrable in the setting of\ndifferential Galois theory under general assumptions. Our result is illustrated\nwith two examples for a stationary Schroedinger equation having a generalized\nHulthen potential and an eigenvalue problem for a traveling front in the\nAllen-Cahn equation.\n

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