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

In: Mathematics Without Boundaries

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  • Michael Gil’

    (Ben Gurion University of the Negev, Department of Mathematics)

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.

Suggested Citation

  • Michael Gil’, 2014. "Stability of Neutral Type Vector Functional Differential Equations with Small Principal Terms," Springer Books, in: Panos M. Pardalos & Themistocles M. Rassias (ed.), Mathematics Without Boundaries, edition 127, pages 287-338, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4939-1124-0_10
    DOI: 10.1007/978-1-4939-1124-0_10
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