ON POSITIVE AND PERIODIC SOLUTIONS OF ONE CLASS OF SYSTEMS OF NONLINEAR ORDINARY DIFFERENTIAL EQUATIONS ON A PLANE
For one class of systems of nonlinear ordinary differential equations on a plane, the properties of positive solutions are investigated as the independent variable t increases. It is proved that any positive solution is defined for all t > 0 and for large values of t is bounded below and above by positive constants that depend only on the coefficients of the system of equations. Based on the obtained estimate, applying the theory of rotation of vector fields, the existence of a positive periodic solution of a given period ω is proved if the coefficients of the system of equations w are periodic in the variable t.