Geodesic
Small periodic solutions of nonlinear systems of differential equations with constant deviation
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 6 (2008), pp. 56-65.

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We consider a nonlinear system of differential equations in a general case with a singular matrix at the derivatives, with a vector deviation which depends on a parameter. We seek for a periodic solution to the system in the set of trigonometric series such that the sequences of their coefficients belong to the space $l_1$. We use the method, representing a space as a direct sum of subspaces, and the method of a fixed point of a nonlinear operator as the main investigation techniques. We reduce the question on the existence of a periodic solution to that of the solvability of an operator equation, whose principal part is defined in a finite-dimensional space.
Keywords: a vector form, an eigen element and an eigenvalue of an operator, a basis of a space, the projecting operator, linear functionals, a fixed point of an operator, the rank of a matrix. 
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M. T. Terekhin. Small periodic solutions of nonlinear systems of differential equations with constant deviation. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 6 (2008), pp. 56-65. http://geodesic.mathdoc.fr/item/IVM_2008_6_a5/

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