Nonimprovable effective sufficient conditions are established for the unique solvability of the periodic problemwhere ω > 0, i : C ([0, ω]) → L ([0, ω]) are linear bounded operators, and q i ∈ L([0, ω]). Statement of problem and formulation of main results. Consider on [0, ω] the systemwith the periodic boundary conditions2) where ω > 0, i : C([0, ω]) → L([0, ω]) are linear bounded operators and q i ∈ L([0, ω]). By a solution of the problem ( 1.1), ( 1.2) we understand a function u ∈ C([0, ω]) which satisfies the system ( 1.1) almost everywhere on [0, ω] and satisfies the conditions ( 1.2).Much work has been carried out on the existence and uniqueness of the solution for a periodic boundary value problem for systems of ordinary differential equations, and many interesting results have been obtained (see, for instance, [1], [2], [3], [4], [5], [6], [7], [8] and the references therein). However, the analogous problem for functional differential equations, even in the case of linear equations, remains little investigated. Mathematics Subject Classification (2000): 34K06, 34K13.

No abstract

Unimprovable efficient sufficient conditions are established for the unique solvability of the periodic problem ([0,ω]) is a linear bounded operator, and q ∈ L ([0,ω]).

No abstract

No abstract