Geodesic
The branching of periodic solutions of inhomogeneous linear differential equations with a the perturbation in the form of small linear term with delay
Žurnal Srednevolžskogo matematičeskogo obŝestva, Tome 18 (2016) no. 3, pp. 61-69.

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In a Banach space by branching theory methods existence and uniqueness of periodic solutions of inhomogeneous linear differential equations with degenerate or identity operator in the derivative and a perturbation in the form of small linear term with delay is proved. The article shows that the periodic solution has a pole at the point $ \varepsilon = 0 $ , and if $ \varepsilon = 0 $ it goes to $2n$–parameter set of periodic solutions. The result is obtained by applying the theory of generalized Jordan sets, that reduces the original problem to the investigation of the Lyapunov-Schmidt resolution system in the root subspace. This resolution system is a non-homogeneous system of linear algebraic equations, which at $ \varepsilon \neq 0 $ has a unique solution, and at a value of $ \varepsilon = 0 $ goes to $2n$-parameter family of solutions.
Keywords: branching of periodic solution, differential equations with delay, generalized Jordan sets, Lyapunov-Schmidt resolution system in the root subspace. 
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P. A. Shamanaev; B. V. Loginov. The branching of periodic solutions of inhomogeneous linear differential equations with a the perturbation in the form of small linear term with delay. Žurnal Srednevolžskogo matematičeskogo obŝestva, Tome 18 (2016) no. 3, pp. 61-69. http://geodesic.mathdoc.fr/item/SVMO_2016_18_3_a5/

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