Small periodic solutions of nonlinear systems of differential equations with constant deviation

M. T. Terekhin

Izvestiâ vysših učebnyh zavedenij. Matematika, no. 6 (2008), pp. 56-65

Résumé

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.

Détail

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.