A uniqueness result for a simple superlinear eigenvalue problem
Analysis of PDEs
2021-03-17 v2 Pattern Formation and Solitons
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.
Cite
@article{arxiv.2004.00829,
title = {A uniqueness result for a simple superlinear eigenvalue problem},
author = {Michael Herrmann and Karsten Matthies},
journal= {arXiv preprint arXiv:2004.00829},
year = {2021}
}
Comments
revised version with enhanced introduction; 21 pages, several figures