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Application of M-matrices in construction of exponential estimates for solutions to the Cauchy problem for systems of linear difference and differential equations

Abstract

We construct a family of exponential estimates for solutions to the Cauchy problem for systems of linear difference and ordinary differential equations and differential equations with aftereffect whose matrices are of a special form. We use the monotone method and properties of nondegenerate M-matrices. We also study some specific examples of systems of equations.

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Correspondence to N. V. Pertsev.

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Original Russian Text © N. V. Pertsev, 2013, published in Matematicheskie Trudy, 2013, Vol. 16, No. 2, pp. 111–141.

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Pertsev, N.V. Application of M-matrices in construction of exponential estimates for solutions to the Cauchy problem for systems of linear difference and differential equations. Sib. Adv. Math. 24, 240–260 (2014). https://doi.org/10.3103/S1055134414040026

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Keywords

  • systems of linear difference and differential equations
  • systems of linear differential equations with aftereffect
  • exponential stability
  • exponential estimates
  • nonnegative matrices
  • nondegenerate M-matrices
  • monotone method