A uniqueness result for a simple superlinear eigenvalue problem
arXiv:2004.00829 · doi:10.1007/s00332-021-09683-8
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.
revised version with enhanced introduction; 21 pages, several figures