Norm estimates for fundamental solutions of neutral type functional differential equations
by Michael Gil'
International Journal of Dynamical Systems and Differential Equations (IJDSDE), Vol. 4, No. 3, 2012

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.

Online publication date: Thu, 18-Oct-2012

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