A uniqueness result for a simple superlinear eigenvalue problem

Michael Herrmann; Karsten Matthies

doi:10.1007/s00332-021-09683-8

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 language	English
Article number	27
Number of pages	29
Journal	Journal of Nonlinear Science
Volume	31
DOIs	https://doi.org/10.1007/s00332-021-09683-8
Publication status	Published - 23 Feb 2021

Keywords

math.AP
nlin.PS

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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. ",

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N2 - 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.

AB - 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.

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KW - nlin.PS

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JO - Journal of Nonlinear Science

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