Publication detail

Singular Initial Value Problem for Certain Classes of Systems of Ordinary Differential Equations

DIBLÍK, J. REBENDA, J. ŠMARDA, Z.

Original Title

Singular Initial Value Problem for Certain Classes of Systems of Ordinary Differential Equations

Czech Title

Singulární počáteční problém pro jisté třídy systémů obyčejných diferenciálních rovnic

English Title

Singular Initial Value Problem for Certain Classes of Systems of Ordinary Differential Equations

Type

journal article

Language

en

Original Abstract

The paper is devoted to the study of the solvability of a singular initial value problem for systems of ordinary differential equations. The main results give sufficient conditions for the existence of solutions in the right-hand neighbourhood of a singular point. In addition, the dimension of the set of initial data generating such solutions is estimated. An asymptotic behavior of solutions is determined as well and relevant asymptotic formulas are derived.

Czech abstract

Příspěvek je věnován studiu řešitelnosti singulární počáteční úlohy pro systémy obyčejných diferenciálních rovnic. Hlavními výsledky jsou postačující podmínky pro existenci řešení v pravém okolí singulárního bodu. Je stanovena i dimense množiny počátečních podmínek generujících taková řešení . Rovněž je popsáno i asymptotické chování řešení včetně stanovení asymptotických tvarů řešení.

English abstract

The paper is devoted to the study of the solvability of a singular initial value problem for systems of ordinary differential equations. The main results give sufficient conditions for the existence of solutions in the right-hand neighbourhood of a singular point. In addition, the dimension of the set of initial data generating such solutions is estimated. An asymptotic behavior of solutions is determined as well and relevant asymptotic formulas are derived.

Keywords

Singular initial value problem; Ordinary differential equations; Asymptotic behavior of solutions

RIV year

2013

Released

09.12.2013

Pages from

1

Pages to

12

Pages count

12

BibTex


@article{BUT103650,
  author="Josef {Diblík} and Josef {Rebenda} and Zdeněk {Šmarda}",
  title="Singular Initial Value Problem for Certain Classes of Systems of Ordinary Differential Equations
",
  annote="The paper is devoted to the study of the solvability of a singular initial value problem for systems of ordinary differential equations. The main results give sufficient conditions for the existence of solutions in the right-hand neighbourhood of a singular point. In addition, the dimension of the set of initial data generating such solutions is estimated. An asymptotic behavior of solutions is determined as well and relevant asymptotic formulas are derived.",
  chapter="103650",
  doi="10.1155/2013/207352",
  howpublished="online",
  number="Article ID 20735",
  volume="2013",
  year="2013",
  month="december",
  pages="1--12",
  type="journal article"
}