Perturbations of the Continuous Spectrum of a Certain Nonlinear Two-Dimensional Operator Sheaf

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F62690094%3A18470%2F21%3A50017896" target="_blank" >RIV/62690094:18470/21:50017896 - isvavai.cz</a>
Result on the web
<a href="https://link.springer.com/article/10.1007/s10958-020-05148-7" target="_blank" >https://link.springer.com/article/10.1007/s10958-020-05148-7</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s10958-020-05148-7" target="_blank" >10.1007/s10958-020-05148-7</a>

Result language
angličtina
Original language name
Perturbations of the Continuous Spectrum of a Certain Nonlinear Two-Dimensional Operator Sheaf
Original language description
In this paper, we consider the operator sheaf − Δ + V+ εℒ ε(λ) + λ2 in the space L2(ℝ2), where the real-valued potential V depends only on the first variable x1, ε is a small positive parameter, λ is the spectral parameter, ℒ ε(λ) is a localized operator bounded with respect to the Laplacian −Δ, and the essential spectrum of this operator is independent of ε and contains certain critical points defined as isolated eigenvalues of the operator −d2dx12+V(x1) in L2(ℝ). The basic result obtained in this paper states that for small values of ε, in neighborhoods of critical points mentioned, isolated eigenvalues of the sheaf considered arise. Sufficient conditions for the existence or absence of such eigenvalues are obtained. The number of arising eigenvalues is determined, and in the case where they exist, the first terms of their asymptotic expansions are found. © 2020, Springer Science+Business Media, LLC, part of Springer Nature.
Czech name
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Czech description
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Type
J<sub>SC</sub> - Article in a specialist periodical, which is included in the SCOPUS database
CEP classification
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OECD FORD branch
10102 - Applied mathematics

Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2021
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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