Paper

Nonlinear and nonlocal eigenvalue problems: variational existence, decay properties, approximation, and universal scaling limits

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Published 2 July 2020 © 2020 IOP Publishing Ltd & London Mathematical Society
, , Citation Michael Herrmann and Karsten Matthies 2020 Nonlinearity 33 4046 DOI 10.1088/1361-6544/ab8350

0951-7715/33/8/4046

Abstract

We study a class of nonlinear eigenvalue problems which involves a convolution operator as well as a superlinear nonlinearity. Our variational existence proof is based on constrained optimization and provides a one-parameter family of solutions with positive eigenvalues and unimodal eigenfunctions. We also discuss the decay properties and the numerical computations of those eigenfunctions, and conclude with two asymptotic results concerning small and large eigenvalues.

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10.1088/1361-6544/ab8350