Title: Norm estimates for fundamental solutions of neutral type functional differential equations

Authors: Michael Gil'

Addresses: Department of Mathematics, Ben Gurion University of the Negev, P.0. Box 653, Beer-Sheva 84105, Israel

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.

Keywords: functional differential equations; neutral type equations; nonlinear equations; causal mappings; stability.

DOI: 10.1504/IJDSDE.2012.049904

International Journal of Dynamical Systems and Differential Equations, 2012 Vol.4 No.3, pp.255 - 273

Published online: 18 Oct 2012 *

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