On the Malmquist Theorem for Solutions of Differential Equations in the Neighborhood of an Isolated Singular Point

The statement of the Malmquist theorem (1913) about the growth of meromorphic solutions of the differential equation , where P(z, f) and Q(z, f) are polynomials in all variables, is proved in the case of solutions with isolated singular point at infinity. __________ Translated from Ukrains'kyi Matematychnyi Zhurnal, Vol. 57, No. 4, pp. 505–513, April, 2005.