Abstract:
The problem of a priori estimate and existence of periodic solutions for a two-dimensional system of nonlinear ordinary second-order differential equations is examined. In terms of the properties of the principal nonlinear part, a theorem on a priori estimate of periodic solutions is formulated and proved. Under the conditions of the a priori estimate, a theorem on necessary and sufficient conditions for the existence of periodic solutions is proved.
Keywords:periodic solution, positive homogeneous mapping, a priori estimate, vector field, degree of a vector field, homotopic pairs of mappings