Singular Initial Value Problem for Certain Classes of Systems of Ordinary Differential Equations
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 s...
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2013-01-01
|
| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2013/207352 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832552411889139712 |
|---|---|
| author | Josef Diblík Josef Rebenda Zdeněk Šmarda |
| author_facet | Josef Diblík Josef Rebenda Zdeněk Šmarda |
| author_sort | Josef Diblík |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-119309e086ed44e794b6056ebef7f640 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-119309e086ed44e794b6056ebef7f6402025-02-03T05:58:36ZengWileyAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/207352207352Singular Initial Value Problem for Certain Classes of Systems of Ordinary Differential EquationsJosef Diblík0Josef Rebenda1Zdeněk Šmarda2Department of Mathematics and Descriptive Geometry, Faculty of Civil Engineering, Brno University of Technology, Veveří 331/95, 602 00 Brno, Czech RepublicCEITEC BUT, Brno University of Technology, Technická 3058/10, 61600 Brno, Czech RepublicBrno University of Technology, Department of Mathematics, Faculty of Electrical Engineering and Communication, Technická 8, 61600 Brno, Czech RepublicThe 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.http://dx.doi.org/10.1155/2013/207352 |
| spellingShingle | Josef Diblík Josef Rebenda Zdeněk Šmarda Singular Initial Value Problem for Certain Classes of Systems of Ordinary Differential Equations Abstract and Applied Analysis |
| title | Singular Initial Value Problem for Certain Classes of Systems of Ordinary Differential Equations |
| title_full | Singular Initial Value Problem for Certain Classes of Systems of Ordinary Differential Equations |
| title_fullStr | Singular Initial Value Problem for Certain Classes of Systems of Ordinary Differential Equations |
| title_full_unstemmed | Singular Initial Value Problem for Certain Classes of Systems of Ordinary Differential Equations |
| title_short | Singular Initial Value Problem for Certain Classes of Systems of Ordinary Differential Equations |
| title_sort | singular initial value problem for certain classes of systems of ordinary differential equations |
| url | http://dx.doi.org/10.1155/2013/207352 |
| work_keys_str_mv | AT josefdiblik singularinitialvalueproblemforcertainclassesofsystemsofordinarydifferentialequations AT josefrebenda singularinitialvalueproblemforcertainclassesofsystemsofordinarydifferentialequations AT zdeneksmarda singularinitialvalueproblemforcertainclassesofsystemsofordinarydifferentialequations |