On spectral properties of the Sturm-Liouville operator with power nonlinearity
type: Item
instance of: scholarly article
title: On spectral properties of the Sturm-Liouville operator with power nonlinearity
zbMATH Open document ID: 1420.34099
published in: Monatshefte für Mathematik
publication date: 2019-01-22T00:00:00Z
review text: The eigenvalue problem for the equation \[y''=(\lambda-\alpha |y|^{2q})y\] with boundary conditions $y(0)=0=y(h)$ where $y'(0)=p$ and $\alpha, q, p>0$ is considered for real $\lambda$. It is shown that there are infinitely many isolated negative as well as infinitely many isolated positive eigenvalues. Asymptotic approximations for the eigenvalues are given, periodicity of the eigenfunctions is proved and the zeros and periods of the eigenfunctions determined.
Mathematics Subject Classification ID: 34L05
Mathematics Subject Classification ID: 34L20
Mathematics Subject Classification ID: 34L15
Mathematics Subject Classification ID: 34B24
zbMATH DE Number: 7004946
zbMATH Keywords: Sturm-Liouville theory
zbMATH Keywords: asymptotic analysis
zbMATH Keywords: nonlinear eigenvalue problem
author: D. V. Valovik
reviewed by: Bruce A. Watson
MaRDI profile type: Publication
full work available at URL: s00605-017-1124-0
OpenAlex ID: W2765592443
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DOI: 10.1007/S00605-017-1124-0
description: scientific article; zbMATH DE number 7004946