Global \(L^ 2\)-bifurcation of nonlinear Sturm-Liouville problems
type: Item
instance of: scholarly article
title: Global \(L^ 2\)-bifurcation of nonlinear Sturm-Liouville problems
zbMATH Open document ID: 0848.34016
DOI: 10.1007/BF00917873
author: Tetsutaro Shibata
published in: ZAMP. Zeitschrift für angewandte Mathematik und Physik
publication date: 1996-01-10T00:00:00Z
review text: In this paper the author considers the nonlinear Sturm-Liouville problem \(-u''(x) = f(u(x)) - \mu u(x)\), \(u(0) = u(1)\), \(f\) odd and \(C^1\), \(\mu > \pi^2\). Under some growth conditions he shows that an asymptotic formula previously obtained for the pure power case [Forum Math. 7, 207-224 (1995; Zbl 0818.34016)] holds also in this case.
Mathematics Subject Classification ID: 34B24
Mathematics Subject Classification ID: 34C23
Mathematics Subject Classification ID: 37G99
zbMATH DE Number: 831609
zbMATH Keywords: nonlinear Sturm-Liouville problem
zbMATH Keywords: asymptotic formula
reviewed by: Pierluigi Zezza
MaRDI profile type: Publication
cites work: Upper and lower bounds for eigenvalues of nonlinear elliptic equations: I. The lowest eigenvalue
cites work: Le nombre de solutions de certains problèmes semi-linéaires elliptiques
cites work: Nonlinear scalar field equations. I: Existence of a ground state
cites work: On spectral asymptotics and bifurcation for elliptic operators with odd superlinear term
cites work: Nodal properties and variational characterizations of solutions to nonlinear Sturm-Liouville problems
cites work: Spectral asymptotics for nonlinear Sturm-Liouville problems
description: scientific article; zbMATH DE number 831609