Nonlinear and Nonlocal Eigenvalue Problems: variational existence, decay properties, approximation, and universal scaling limits

Michael Herrmann; Karsten Matthies

doi:10.1088/1361-6544/ab8350

Nonlinear and Nonlocal Eigenvalue Problems: variational existence, decay properties, approximation, and universal scaling limits

Michael Herrmann, Karsten Matthies

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3 Citations (SciVal)

133 Downloads (Pure)

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.

Original language	English
Pages (from-to)	4046–4074
Number of pages	29
Journal	Nonlinearity
Volume	33
Issue number	8
DOIs	https://doi.org/10.1088/1361-6544/ab8350
Publication status	Published - Aug 2020

Bibliographical note

Publisher Copyright:
© 2020 IOP Publishing Ltd & London Mathematical Society.

Keywords

math-ph
math.MP
45G10, 45M05, 47J10, 49R05
nonlinear eigenvalue problems
asymptotic analysis of nonlinear integral operators
nonlocal coherent structures

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics
General Physics and Astronomy
Applied Mathematics

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10.1088/1361-6544/ab8350

1911.06018v2.pdf
(c) 2020 IOP Publishing Limited & London Mathematical Society. This is an author-created, un-copyedited version of an article published in Nonlinearity. IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The Version of Record is available online at https://iopscience.iop.org/article/10.1088/1361-6544/ab8350/pdf
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Cite this

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Nonlinear and Nonlocal Eigenvalue Problems: variational existence, decay properties, approximation, and universal scaling limits

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

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