Geodesic
The branching of periodic solutions of inhomogeneous linear differential equations with degenerate or identity operator in the derivative and the disturbance in the form of small linear term
Žurnal Srednevolžskogo matematičeskogo obŝestva, Tome 18 (2016) no. 1, pp. 45-53

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In a Banach space existence and uniqueness of periodic solutions of inhomogeneous linear differential equations with degenerate or identity operator in the derivative and a disturbance in the form of small linear term proved by branching theory methods. The article shows that the periodic solution has a pole at the point $ \varepsilon = 0 $ , and if $ \varepsilon = 0 $ the solution goes to $2n$–parameter set of periodic solutions. The result is obtained by applying the theory of generalized Jordan sets, reducing the original problem to the investigation of the Lyapunov-Schmidt resolution system in the root subspace. In this resolution the system is divided into two non-homogeneous systems of linear algebraic equations. These systems have the only solution when $\varepsilon\neq 0$; when $\varepsilon = 0 $ they have $n$-parameter set of solutions, respectively.
Keywords: differential equations in Banach spaces , generalized Jordan sets, Lyapunov-Schmidt resolution system in the root subspace. 
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     title = {The branching of periodic solutions of inhomogeneous linear differential equations with degenerate or identity operator in the derivative and the disturbance in the form of small linear term},
     journal = {\v{Z}urnal Srednevol\v{z}skogo matemati\v{c}eskogo ob\^{s}estva},
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A. A. kjashkin; B. V. Loginov; P. A. Shamanaev. The branching of periodic solutions of inhomogeneous linear differential equations with degenerate or identity operator in the derivative and the disturbance in the form of small linear term. Žurnal Srednevolžskogo matematičeskogo obŝestva, Tome 18 (2016) no. 1, pp. 45-53. http://geodesic.mathdoc.fr/item/SVMO_2016_18_1_a5/