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

Authors:

Institution:

(1) A. Razmadze Mathematical Institute, Georgian Academy of Sciences, M. Aleksidze Str. 1, 0193 Tbilisi, Georgia;(2) Present address: Mathematical Institute, Academy of Sciences of the Czech Republic, Žižkova 22, CZ-616 62 Brno, Czech Republic

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]). Received: 11 June 2005

Keywords:

Mathematics Subject Classification (2000)" target="_blank">Mathematics Subject Classification (2000) 34K06 34K13

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