On a periodic boundary value problem for third order linear functional differential equations

Unimprovable sufficient conditions are established for the unique solvability of the periodic problem u‴(t)=∑i=02ℓi(u(i))(t)+q(t),u(j)(0)=u(j)(ω)+cj(j=0,2¯), where ℓi:C([0,ω])→L([0,ω])ℓi:C([0,ω])→L([0,ω]) are the linear bounded operators, q∈L([0,ω])q∈L([0,ω]) and cj∈Rcj∈R.