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 Review articles Inverse problems of dynamics and problems of control of the motions of material systemsA. S. Galiullin 1535 Ordinary Differential Equations The Cauchy problem for differential equations with retarded argumentN. V. Azbelev, L. F. Rakhmatullina 1542 Necessary conditions for the extremum of a functionV. G. Boltyanskii 1553 On the question of solutions that are close to continuous ones in a system of conditionally stable type with a small parameter multiplying the derivativesA. B. Vasil'eva 1560 Positive cycles in a system with a limiting factorYu. I. Gil'derman, K. N. Kudrina 1569 Nonstability of the exponent of exponential separatedness of the solutions of a system of differential equations and nonsymmetry of the relation of almost reducibility of systems of differential equations with integral separatedness of the solutionsS. A. Grishin 1577 Dynamical systems with aftereffectV. K. Dubolar' 1587 A certain method of solving linear differential equations of order $n\leq +\infty$A. A. Tunda 1598 Partial Differential Equations Fractional powers of elliptic operators and isomorphism of classes of differentiable functionsSh. A. Alimov 1609 The branchings of the solutions of a certain class of nonlinear partial differential equationsYa. V. Bykov, K. A. Kiriy 1627 Well-posed formulation of a mixed problem for the nonstationary transport equationYu. A. Kuznetsov, S. F. Morozov 1639 The fundamental solutions of a certain class of elliptic-parabolic second order equationsL. P. Kuptsov 1649 Finite difference equations Difference methods of solving ill-posed Cauchy problems for evolution equations in a complex $B$-spaceA. B. Bakushinskii 1661 The method of successive approximations in connection with second order differential equationsYa. B. Kadymov, G. B. Abdulov 1669 Factorized Rothe schemes for quasilinear parabolic equationsA. D. Lyashko 1674 Short Communications Investigation of the qualitative behavior of the trajectories of a certain system of differential equationsV. T. Borukhov 1682 The stability of relay systemsA. Kh. Gelig 1684 On the theory of optimal processes in linear systemsS. Daiovich 1687 Limit cycles in the case of the centerM. V. Dolov 1691 The stability of multicomponent periodic motionsV. I. Zubov 1693 The Čaplygin problem for a certain first order differential equationG. S. Krechetov 1695 Regularization of equations with a closed operatorO. A. Liskovets 1698 The boundedness and unboundedness of the solutions of a second order ordinary differential equationS. N. Olekhnik 1701 The stability of certain systems with transformed argumentV. P. Skripnik 1705 Investigation of the trajectories of a certain dynamical systemV. F. Filiptsov 1709