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Документ Properties of solutions of a heterogeneous differential equation of the second order(2019) Mulyava, Oksana; Sheremeta, Miroslav; Trukhan, Yu. S.Suppose that a power seriesA(z) =∑∞n=0anznhas the radius of convergenceR[A]∈[1,+∞].For a heterogeneous differential equationz2w′′+ (β0z2+β1z)w′+ (γ0z2+γ1z+γ2)w=A(z)with complex parameters geometrical properties of its solutions (convexity, starlikeness and close-to-convexity) in the unit disk are investigated. Two cases are considered: ifγ26=0 andγ2=0. Wealso consider cases when parameters of the equation are realnumbers. Also we prove that for asolutionfof this equation the radius of convergenceR[f]equals toR[A]and the recurrent formulasfor the coefficients of the power series off(z)are found. For entire solutions it is proved that theorder of a solutionfis not less then the order ofA(̺[f]≥̺[A]) and the estimate is sharp. The sameinequality holds for generalized orders (̺αβ[f]≥̺αβ[A]). For entire solutions of this equation thebelonging to convergence classes is studied. Finally, we consider a linear differential equation of theendless order∞∑n=0ann!w(n)=Φ(z), and study a possible growth of its solutions.Документ On Hadamard compositions of Dirihlet series and Dirihlet series absolutely converging in half-plane(2019) Mulyava, Oksana; Sheremeta, MiroslavIn terms of generalized orders the growth of this composition and their derivatives is investigated. A relation between the behavior of the maximal terms of the Hadamard composition of the derivatives and of the derivative of the Hadamard composition is established.Документ Remarks to relative growth of entire dirichlet series(2019) Mulyava, Oksana; Sheremeta, MiroslavThe growth of F with respect to G is studied through the generalized order. Formulas are found for the finding these quantities.Документ On the Relative Growth of Dirichlet Series with Zero Abscissa of Absolute Convergence(2021) Mulyava, OksanaLet F and G be analytic functions given by Dirichlet series with exponents increasing to + ∞ and zero abscissa of absolute convergence.The growth of F with respect to G is studied through the generalized order. Formulas are found for the finding these quantities.