A uniqueness result for a simple superlinear eigenvalue problem

Michael Herrmann, Karsten Matthies

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Abstract

We study the eigenvalue problem for a superlinear convolution operator in the special case of bilinear constitutive laws and establish the existence and uniqueness of a one-parameter family of nonlinear eigenfunctions under a topological shape constraint. Our proof uses a nonlinear change of scalar parameters and applies Krein-Rutmann arguments to a linear substitute problem. We also present numerical simulations and discuss the asymptotics of two limiting cases.
Original languageEnglish
Article number27
Number of pages29
JournalJournal of Nonlinear Science
Volume31
DOIs
Publication statusPublished - 23 Feb 2021

Keywords

  • math.AP
  • nlin.PS

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