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.
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