Stability of neutral type vector functional differential equations with small principal terms

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2 Scopus citations

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.

Original languageEnglish
Title of host publicationMathematics Without Boundaries
Subtitle of host publicationSurveys in Interdisciplinary Research
PublisherSpringer New York
Pages287-338
Number of pages52
ISBN (Electronic)9781493911240
ISBN (Print)1493911236, 9781493911233
DOIs
StatePublished - 1 Apr 2014

Keywords

  • Absolute stability
  • Bohl-Perron principle
  • Causal mappings
  • Exponential stability
  • Functional differential equations
  • L <sup>p</sup>-stability
  • Linear and nonlinear equations
  • Neutral type equations

ASJC Scopus subject areas

  • Mathematics (all)

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