On a periodic boundary value problem for cyclic feedback type linear functional differential systems. (English) Zbl 1132.34045
The authors are interested in the study of the following system
\[ \begin{aligned} u_i^{\prime\prime}(t)&= l_i(u_{i+1})(t) +q_i(t), \quad i=1,\dots,n-1,\\ u_n^{\prime\prime}& =l_n(u_1)(t)+q_n(t)\end{aligned} \]
with periodic conditions
\[ u_j(t+\omega)=u_j(t),\quad j=1,\dots,n,\;t\in\mathbb R. \]
They give integral sufficient conditions for unique solvability of this problem in case that \( l_i \) are monotone linear operators.
\[ \begin{aligned} u_i^{\prime\prime}(t)&= l_i(u_{i+1})(t) +q_i(t), \quad i=1,\dots,n-1,\\ u_n^{\prime\prime}& =l_n(u_1)(t)+q_n(t)\end{aligned} \]
with periodic conditions
\[ u_j(t+\omega)=u_j(t),\quad j=1,\dots,n,\;t\in\mathbb R. \]
They give integral sufficient conditions for unique solvability of this problem in case that \( l_i \) are monotone linear operators.
Reviewer: Mustapha Yebdri (Tlemcen)
MSC:
| 34K10 | Boundary value problems for functional-differential equations |
| 34K13 | Periodic solutions to functional-differential equations |
| 34K06 | Linear functional-differential equations |
