ON A PRIORI ESTIMATE OF PERIODIC SOLUTIONS OF THE SYSTEM OF ORDINARY DIFFERENTIAL EQUATIONS OF THE SECOND ORDER WITH THE MAIN POSITIVELY HOMOGENEOUS NONLINEARITY

For the system of ordinary differential equations of the second order with the main positively homogeneous nonlinearity, an a priori estimate of periodic solutions of a fixed period is investigated. New conditions of a priori estimate are found, in which the influence of the properties of the main nonlinear part, including its set of zeros, is mediated by functional estimates from above and below. The feasibility of the new conditions is investigated for three types of nonlinearities.