Periodic solutions of evolutionary equations

An analog of L. Cesari's method for a very general class of evolutionary equations is investigated. A result is proved concerning the coincidence of rotation of a Cesari field with the rotation of a translation operator (on boundaries of naturally corresponding regions), and Galerkin's method of obtaining periodic solutions is studied. The results obtained are new for ordinary differential equations.Translated from Matematicheskie Zametki, Vol. 9, No. 6, pp. 651–662, June, 1971.