Terekhin M. T.

We investigate the case where conditions for the existence of a nonzero periodic solution of a system of ordinary differential equations are determined by the properties of elements of the matrix of linear approximation and the properties of nonlinear terms.

We prove a theorem on the existence of a nonzero periodic solution of a system of differential equations with deviation that depends both on an unknown function and on its derivative. This result is obtained for the case where the matrix of linear approximation has zero and imaginary eigenvalues if the parameter takes a critical value.

We prove theorem, in which basic conditions for the existence of nontrivial periodic solutions are formulated in terms of the properties of the elements of the matrix of a linear approximation to a system.