Geodesic
On periodic boundary-value problems for systems of functional-differential equations
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of International Symposium “Differential Equations–2016”, Perm, May 17-18, 2016, Tome 132 (2017), pp. 16-19.

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We obtain necessary and sufficient conditions for the existence of a unique solution to a periodic boundary-value problem for all systems of first-order functional-differential equations from a given family of systems. Families of systems of functional-differential equations are determined by the norms of positive functional operators of equations of the system. The verification of necessary and sufficient conditions of the existence of a unique periodic solution for all systems from a given family consists of the verification of positivity of a finite number of a real-valued functions defined on a finite-dimensional set.
Keywords: functional-differential equation, boundary-value problem, exact solvability condition, periodic boundary-value problem. 
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     author = {E. I. Bravyi},
     title = {On periodic boundary-value problems for systems of functional-differential equations},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {16--19},
     publisher = {mathdoc},
     volume = {132},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2017_132_a3/}
}
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E. I. Bravyi. On periodic boundary-value problems for systems of functional-differential equations. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of International Symposium “Differential Equations–2016”, Perm, May 17-18, 2016, Tome 132 (2017), pp. 16-19. http://geodesic.mathdoc.fr/item/INTO_2017_132_a3/