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Estimates for the Cauchy function of linear singular differential equations and some applications

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Abstract

For higher-order linear singular equations, we find sharp estimates for the Cauchy function and its partial derivatives. We use these estimates to study the properties of solutions of singular differential inequalities and obtain optimal sufficient conditions for the unique solvability of the linear singular Cauchy problem.

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Authors and Affiliations

  1. Florida Institute of Technology, Melbourne, USA

    T. I. Kiguradze

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  1. T. I. Kiguradze
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Original Russian Text © T.I. Kiguradze, 2010, published in Differentsial’nye Uravneniya, 2010, Vol. 46, No. 1, pp. 29–46.

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Kiguradze, T.I. Estimates for the Cauchy function of linear singular differential equations and some applications. Diff Equat 46, 30–47 (2010). https://doi.org/10.1134/S0012266110010052

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  • DOI: https://doi.org/10.1134/S0012266110010052

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