Norm estimates for fundamental solutions of neutral type functional differential equations

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Abstract

This paper deals with a vector autonomous neutral type functional differential equation. Estimates for various norms of the fundamental solution are established. By the derived estimates we obtain the stability conditions for equations with non-linear causal mappings. Equations with causal mappings include differential-delay, integro-differential, and other equations. Our stability conditions are explicitly formulated in terms of the entries of the characteristic matrices and Lipschitz constants of non-linearities. The suggested approach is based on a combined use of the recent estimates for the Euclidean norm of matrix-valued functions with some properties of the fundamental solutions.

Original languageEnglish
Pages (from-to)255-273
Number of pages19
JournalInternational Journal of Dynamical Systems and Differential Equations
Volume4
Issue number3
DOIs
StatePublished - 1 Jan 2012

Keywords

  • Causal mappings
  • Functional differential equations
  • Neutral type equations
  • Non-linear equations
  • Stability

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