Asymptotic behavior of the curves in the Fuč'ık spectrum

2016/09/26 by Juan Pablo Pinasco, Ariel Salort, Pinasco, Juan Pablo +1
Mathematics · #Advanced Algebra and Geometry #Algebraic and Geometric Analysis #Analysis of PDEs (math.AP) #Differential Equations and Boundary Problems #Differential Equations and Numerical Methods #FOS: Mathematics #Geometric Analysis and Curvature Flows #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.1609.08193

openalex publication_date 2016/09/26 · openalex created_date 2024/04/11 · openalex updated_date 2026/07/28

Abstract

In this work we study the asymptotic behavior of the curves of the Fuč'ık spectrum for weighted second order linear ordinary differential equations. We prove a Weyl type asymptotic behavior of the hyperbolic type curves in the spectrum in terms of some integrals of the weights. We present an algorithm which computes the intersection of the Fuč'ık spectrum with rays through the origin, and we compare their values with the asymptotic ones.

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