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  • Research Article
  • Open Access

Abstract differential inequalities and the Cauchy problem for infinite-dimensional linear functional differential equations

Journal of Inequalities and Applications20052005:348549

  • Received: 27 August 2003
  • Published:


We establish optimal, in a sense, unique solvability conditions of the Cauchy problem for a wide class of linear functional differential equations in a Banach space with a solid wedge. The conditions are formulated in terms of certain abstract functional differential inequalities.

Authors’ Affiliations

Institute of Mathematics, National Academy of Sciences of Ukraine, 3 Tereschenkovskaya, Kiev, 01601, Ukraine
Mathematical Institute, Czech Academy of Sciences, Žižkova 22, Brno, 61662, Czech Republic