Left-Definite Sturm–Liouville Problems
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TLDR
In this paper, the authors give an algorithm for computing the eigenvalues of a left-definite regular self-adjoint Sturm-Liouville problem with an arbitrary coupled boundary condition.About:
This article is published in Journal of Differential Equations.The article was published on 2001-11-20 and is currently open access. It has received 43 citations till now. The article focuses on the topics: Sturm–Liouville theory & Robin boundary condition.read more
Citations
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Journal ArticleDOI
A General Left-Definite Theory for Certain Self-Adjoint Operators with Applications to Differential Equations
Lance L. Littlejohn,R. Wellman +1 more
TL;DR: In this article, it was shown that any self-adjoint operator A (bounded or unbounded) in a Hilbert space H=(V,(·,·)) that is bounded below generates a continuum of Hilbert spaces {Hr}r>0 and a spectrum of selfadjoint operators {Ar} r>0.
Book ChapterDOI
Sturm’s 1836 Oscillation Results Evolution of the Theory
TL;DR: In this paper, Sturm's oscillation theorems on comparison, separation, and indexing the number of zeros of eigenfunctions have been examined for the second-order case.
Journal ArticleDOI
Bounds on the non-real spectrum of differential operators with indefinite weights
TL;DR: In this paper, it was shown that a bounded additive perturbation leads to an operator whose non-real spectrum is contained in a compact set and with definite type real spectrum outside this set.
Journal ArticleDOI
Singular left-definite Sturm–Liouville problems
Qingkai Kong,H. Wu,Anton Zettl +2 more
TL;DR: In this article, the existence of eigenvalues for singular left-definite Sturm-Liouville problems with an indefinite weight function was established based on the eigenvalue of corresponding right-definitive problems.
Journal ArticleDOI
Spectral analysis of singular ordinary differential operators with indefinite weights
Jussi Behrndt,Friedrich Philipp +1 more
TL;DR: In this article, a perturbation approach was developed to investigate spectral problems for singular ordinary differential operators with indefinite weight functions, which is applied to singular indefinite Sturm-Liouville operators.
References
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Book
Spectral Theory of Ordinary Differential Operators
TL;DR: In this paper, the separation of the Dirac operator was discussed and the Lagrange identity for n>2 was proved for the case of Dirac systems with self-adjoint differential expressions.
Book
Grundzuge Einer Allgemeinen Theorie Der Linearen Integralgleichungen
TL;DR: In this article, a Funktion K(s, t) heise der Kern der Integralgleichungen, i.e., the bestimmende Funktion of a reelle Veranderlichen.
Book
Variational Methods for Eigenvalue Approximation
TL;DR: In this article, the authors provide a common setting for various methods of bounding the eigenvalues of a self-adjoint linear operator and emphasize their relationships, and provide a set of methods of quantifying the relationship between these eigenvectors.