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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

  • Czech description

Classification

  • Type

    J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database

  • CEP classification

  • 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

  • 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