Results 31 to 40 of about 11,899 (198)

Indefinite Sturm-Liouville operators with the singular critical point zero

, 2006
We present a new necessary condition for similarity of indefinite Sturm-Liouville operators to self-adjoint operators. This condition is formulated in terms of Weyl-Titchmarsh $m$-functions.
Karabash, Illya M., Kostenko, Aleksey S.
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Random Sturm–Liouville operators

Applied Mathematics Letters, 2011
Selfadjoint Sturm-Liouville operators $H_ $ on $L_2(a,b)$ with random potentials are considered and it is proven, using positivity conditions, that for almost every $ $ the operator $H_ $ does not share eigenvalues with a broad family of random operators and in particular with operators generated in the same way as $H_ $ but in $L_2(\tilde a,\tilde
openaire   +2 more sources

Eigenvalue Ratios for Sturm-Liouville Operators

Journal of Differential Equations, 1993
This paper deals with estimates for eigenvalue ratios for regular Sturm-Liouville problems \(-[p(x)y']'+q(x)y=\lambda w(x)y\) on a finite interval with Dirichlet boundary conditions. In the general case \(q \geq 0\), the authors prove the upper estimate \(\lambda_ m/ \lambda_ l \leq K \{m/l\} ^ 2/k\) for \(m>l \geq 1\) where \(k\), \(K \geq 0\) are ...
Ashbaugh, Mark S., Benguria Donoso, Rafael   +1 more
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Dissipative Sturm-Liouville Operators with Transmission Conditions [PDF]

Abstract and Applied Analysis, 2013
In this paper we study dissipative Sturm-Liouville operators with transmission conditions. By using Pavlov’s method (Pavlov 1947, Pavlov 1981, Pavlov 1975, and Pavlov 1977), we proved a theorem on completeness of the system of eigenvectors and associated vectors of the dissipative Sturm-Liouville operators with transmission conditions.
Hüseyin Tuna, Aytekin Eryılmaz
openaire   +4 more sources

An inverse spectral problem for the matrix Sturm-Liouville operator on the half-line

, 2014
The matrix Sturm-Liouville operator with an integrable potential on the half-line is considered. We study the inverse spectral problem, which consists in recovering of this operator by the Weyl matrix.
Bondarenko, Natalia
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Periodic Solutions of the Euler-Bernoulli Equation for Vibrations of a Beam with Fixed Ends

Современные информационные технологии и IT-образование, 2020
The problem of time-periodic solutions of the quasilinear equation of forced vibrations of an I-beam with fixed ends is investigated. The nonlinear term and the right-hand side of the equation are time-periodic functions.
Igor Rudakov, Mikhail Zinovyev
doaj   +1 more source

Embedded eigenvalues of Sturm Liouville operators [PDF]

Communications in Mathematical Physics, 1991
The behaviour of embedded eigenvalues for Sturm-Liouville problems in \([0,\infty)\) under local perturbations is studied. If the spectral function has a strictly positive derivative then the embedded eigenvalues either disappear or remain fixed. In this case local perturbations cannot add eigenvalues in the continuous spectrum.
openaire   +2 more sources

Spectral partitions for Sturm-Liouville problems

, 2018
We look for best partitions of the unit interval that minimize certain functionals defined in terms of the eigenvalues of Sturm-Liouville problems. Via \Gamma-convergence theory, we study the asymptotic distribution of the minimizers as the number of ...
Tilli, Paolo, Zucco, Davide
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Wintner-type nonoscillation theorems for conformable linear Sturm-Liouville differential equations [PDF]

Opuscula Mathematica
In this study, we addressed the nonoscillation of th Sturm-Liouville differential equation with a differential operator, which corresponds to a proportional-derivative controller. The equation is a conformable linear differential equation. A Wintner-type
Kazuki Ishibashi
doaj   +1 more source

Regularizing infinite sums of zeta-determinants

, 2014
We present a new multiparameter resolvent trace expansion for elliptic operators, polyhomogeneous in both the resolvent and auxiliary variables. For elliptic operators on closed manifolds the expansion is a simple consequence of the parameter dependent ...
Lesch, Matthias, Vertman, Boris
core   +1 more source