S. Mukhigulashvili and B. Půža

On a Periodic Boundary Value Problem for Cyclic Feedback Type Linear Functional Differential Systems

abstract:
Unimprovable effective sufficient conditions are established for unique solvability of the periodic problem
\begin{align*} u''_i(t) & =\ell_{i}(u_{i+1})(t)+q_i(t) \;\; (i=1,\dots,n-1), \\ u''_n (t) & =\ell_{n}(u_1 )(t) + q_n (t), \\ u_j(t+\omega) & =u_j(t)\;\; (j=1,\dots,n)\;\;\text{for}\;\; t\in R, \end{align*} where $\omega >0$, $\ell_{i}:C_{\omega}\to L_{\omega}$ are linear bounded operators, and $q_i \in L_{\omega}$.

Mathematics Subject Classification: 34K06, 34K13, 34K10

Key words and phrases: Linear functional differential system, cyclic feedback type system, periodic problem