Stability of Neutral Type Vector Functional Differential Equations with Small Principal Terms

Michael Gil’ ()
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Michael Gil’: Ben Gurion University of the Negev, Department of Mathematics

A chapter in Mathematics Without Boundaries, 2014, pp 287-338 from Springer

Abstract: Abstract This paper is devoted to the stability of neutral type functional differential equations whose principal terms are small in a certain sense. We derive the explicit conditions for the exponential and absolute stabilities, as well as for the L p -stability. Besides, solution estimates for the considered equations are established. They provide bounds for the regions of attraction of steady states. We also consider some classes of equations with neutral type linear parts and nonlinear causal mappings. These equations include differential, differential-delay, integro-differential, and other traditional equations. The main methodology presented in the paper is based on a combined usage of the recent norm estimates for matrix-valued functions with the generalized Bohl–Perron principle for neutral type functional differential equations. Our approach enables us to apply the well-known results of the theory of matrices to the stability analysis.

Keywords: Functional differential equations; Neutral type equations; Linear and nonlinear equations; Exponential stability; Absolute stability; L p -stability; Causal mappings; Bohl–Perron principle; 34K20; 34K99; 93D05; 93D25 (search for similar items in EconPapers)
Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4939-1124-0_10

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DOI: 10.1007/978-1-4939-1124-0_10

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