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

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  • Josef Diblík
  • Josef Rebenda
  • Zdeněk Šmarda

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.

Suggested Citation

  • Josef Diblík & Josef Rebenda & Zdeněk Šmarda, 2013. "Singular Initial Value Problem for Certain Classes of Systems of Ordinary Differential Equations," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-12, December.
    • Handle: RePEc:hin:jnlaaa:207352
    DOI: 10.1155/2013/207352
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