Abstract and Applied Analysis

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

Josef Diblík, Josef Rebenda, and Zdeněk Šmarda

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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. The method of functions defined implicitly and the topological method (Ważewski's method) are used in the proofs. The results generalize some previous ones on singular initial value problems for differential equations.

Article information

Source
Abstr. Appl. Anal., Volume 2013, Special Issue (2013), Article ID 207352, 12 pages.

Dates
First available in Project Euclid: 26 February 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1393449717

Digital Object Identifier
doi:10.1155/2013/207352

Mathematical Reviews number (MathSciNet)
MR3139477

Zentralblatt MATH identifier
1296.34049

Citation

Diblík, Josef; Rebenda, Josef; Šmarda, Zdeněk. Singular Initial Value Problem for Certain Classes of Systems of Ordinary Differential Equations. Abstr. Appl. Anal. 2013, Special Issue (2013), Article ID 207352, 12 pages. doi:10.1155/2013/207352. https://projecteuclid.org/euclid.aaa/1393449717


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