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On a periodic boundary value problem for cyclic feedback type linear functional differential systems

Abstract.

Nonimprovable effective sufficient conditions are established for the unique solvability of the periodic problem

$$ u^{\prime }_{i} (t) = {\ell }_{i} (u_{{i + 1}} )(t) + q_{i} (t)\quad (i = \overline{{1,n - 1}} ), $$
$$ u^{\prime }_{n} (t) = {\ell }_{n} (u_{1} )(t) + q_{n} (t), $$
$$ u_{j} (0) = u_{j} (\omega )\quad (j = \overline{{1,n}} ), $$

where ω  >  0, ℓ i : C([0, ω])→ L([0,ω]) are linear bounded operators, and q i L([0, ω]).

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Correspondence to Sulkhan Mukhigulashvili.

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Received: 11 June 2005

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Mukhigulashvili, S. On a periodic boundary value problem for cyclic feedback type linear functional differential systems. Arch. Math. 87, 255–260 (2006). https://doi.org/10.1007/s00013-006-1621-1

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Mathematics Subject Classification (2000).

  • 34K06
  • 34K13