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Annali di Matematica Pura ed Applicata (1923 -)

, Volume 116, Issue 1, pp 177–187 | Cite as

Integrodifferential systems with infinitely many delays

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Summary

In this paper we consider the initial-value problems: (P1)X(t)=(AX)(t) for t>0, X(0+)=I, X(t)=0 for t<0 and (P2) Y(t)=(QY)(t) for t>0, Y(0+)=I, Y(t)=0 for t<0, where A and Q are linear specified operators, I and0 — the identity and null matrices of order n, and X(t), Y(t) are unknown functions whose values are square matrices of order n. Sufficient conditions are established under which the problems (P1) and (P2) have the same unique solution, locally summable on the half-axis t ⩾0. Using this fact and some properties of the Laplace transform we find a new proof for the variation of constants formula given in[1, 2]. On the basis of this formula we derive certain results concerning a class of integrodifferential systems with infinite delay.

Keywords

Infinite Delay Constant Formula Integrodifferential System 

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Copyright information

© Fondazione Annali di Matematica Pura ed Applicata (1923 -) 1978

Authors and Affiliations

  • N. Luca
    • 1
  1. 1.IaşiRomânia

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