Small periodic solutions of nonlinear systems of differential equations with constant deviation |
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Authors: | M T Terekhin |
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Institution: | (1) Ryazan State University, ul. Svobody 46, Ryazan, 390000, Russia |
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Abstract: | 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. |
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Keywords: | vector form eigenelement and eigenvalue of an operator basis of a space projecting operator linear functionals fixed point of an operator rank of a matrix |
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