Sturm-Liouville matrix differential systems with singular leading coefficient

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

Sturm-Liouville matrix differential systems with singular leading coefficient

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

Sturm-Liouville matrix differential systems with singular leading coefficient

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/GA16-00611S" target="_blank" >GA16-00611S: Hamiltonovské a symplektické systémy: oscilační a spektrální teorie</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2017

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Annali di Matematica Pura ed Applicata. Series IV

ISSN

0373-3114

e-ISSN

—

Svazek periodika

196

Číslo periodika v rámci svazku

3

Stát vydavatele periodika

DE - Spolková republika Německo

Počet stran výsledku

19

Strana od-do

1165-1183

Kód UT WoS článku

000402126700017

EID výsledku v databázi Scopus

2-s2.0-84988358915