Title: Some properties of meromorphic solutions of linear differential equation with meromorphic coefficients
Abstract: Estimations of growth of the meromorphic solutions of linear differential equations with meromorphic coefficients in terms of Nevanlinna's characteristics have been obtained.Namely, it is proven that if in the equation f (n) +a n-1 (z)f (n-1) +. ..+a s+1 (z)f s+1 +. ..+a 0 (z)f = 0 the coefficients a j (z), j = 0, 1, . . ., n -1, are meromorphic functions in C, such that the coefficient a j (z), j = s+1, s+2, . . ., n-1, grow slower than the coefficients a s does, then the equation can have at most s linearly independent meromorphic solutions, the growth of which is restricted by the growth of the coefficient a s .