Sturm-Liouville matrix differential systems with singular leading coefficient
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14310%2F17%3A00094553" target="_blank" >RIV/00216224:14310/17:00094553 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1007/s10231-016-0611-6" target="_blank" >http://dx.doi.org/10.1007/s10231-016-0611-6</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s10231-016-0611-6" target="_blank" >10.1007/s10231-016-0611-6</a>
Alternative languages
Result language
angličtina
Original language name
Sturm-Liouville matrix differential systems with singular leading coefficient
Original language description
In this paper we study a general even order symmetric Sturm-Liouville matrix differential equation, whose leading coefficient may be singular on the whole interval under consideration. Such an equation is new in the current literature, as it is equivalent with a system of Sturm-Liouville equations with different orders. We identify the so-called normal form of this equation, which allows to transform this equation into a standard (controllable) linear Hamiltonian system. Based on this new transformation we prove that the associated eigenvalue problem with Dirichlet boundary conditions possesses all the traditional spectral properties, such as the equality of the geometric and algebraic multiplicities of the eigenvalues, orthogonality of the eigenfunctions, the oscillation theorem and Rayleigh's principle, and the Fourier expansion theorem. We also discuss sufficient conditions, which allow to reduce a general even order symmetric Sturm-Liouville matrix differential equation into the normal form. Throughout the paper we provide several examples, which illustrate our new theory.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
<a href="/en/project/GA16-00611S" target="_blank" >GA16-00611S: Hamiltonian and symplectic systems: oscillation and spectral theory</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2017
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Annali di Matematica Pura ed Applicata. Series IV
ISSN
0373-3114
e-ISSN
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Volume of the periodical
196
Issue of the periodical within the volume
3
Country of publishing house
DE - GERMANY
Number of pages
19
Pages from-to
1165-1183
UT code for WoS article
000402126700017
EID of the result in the Scopus database
2-s2.0-84988358915