Nontrivial Fučík spectrum of one non-selfadjoint operator
type: Item
instance of: scholarly article
title: Nontrivial Fučík spectrum of one non-selfadjoint operator
zbMATH Open document ID: 1161.34009
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2008-10-21T00:00:00Z
review text: The Fučík spectrum of the boundary value problem \[ u''(x)=\begin{cases} \alpha u^+(x)-\beta u^-(x), & x\in (0,\pi)\\ u'(0) =u'(\xi),\;u(\pi)=u(\eta), & \xi\in (0,\pi),\;\eta \in (0,\pi) \end{cases} \] is the set of all pairs \((\alpha,\beta )\) of real numbers for which this problem has a nontrivial solution. The left-hand side of this problem is a linear but non-selfadjoint operator, however with only real spectrum. The author gives explicit formulas for the Fučík spectrum as well as a number of pictures with different parts of this spectrum. It is explained and discussed how this behaviour differs from that of the Fučík spectrum of the Sturm-Liouville operator with self-adjoint boundary conditions.
Mathematics Subject Classification ID: 34B15
Mathematics Subject Classification ID: 34B10
Mathematics Subject Classification ID: 34B08
Mathematics Subject Classification ID: 34L05
zbMATH DE Number: 5355039
zbMATH Keywords: Fučík spectrum
zbMATH Keywords: multi-point boundary value problem
zbMATH Keywords: non-selfadjoint operator
author: G. Holubová
author: Petr Necesal
MaRDI profile type: Publication
full work available at URL: j.na.2007.08.066
OpenAlex ID: W1996573879
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DOI: 10.1016/J.NA.2007.08.066
description: scientific article; zbMATH DE number 5355039