A uniqueness result for a simple superlinear eigenvalue problem

Michael Herrmann, Karsten Matthies

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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
JournalJournal of Nonlinear Science
Publication statusAcceptance date - 29 Dec 2020


  • math.AP
  • nlin.PS

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