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 A linear optimal control problemV. G. Boltyanskii 783 A necessary and sufficient criterion, and the precise asymptotics of stability in the first approximationR. È. Vinograd 800 The existence of a family of periodic solutions of a system of two second order differential equationsI. A. Pasynkova 814 On the question of the stability of quasiperiodic motionsA. S. Gurtovnik, Yu. I. Neimark 824 A generalization of Ljapunov's first theorem on stability to certain classes of differential equations in a Banach spaceE. N. Gersht 833 The stability of the state of equilibrium of systems of differential equationsM. M. Khapaev 848 On the question of stability under constantly acting perturbationsN. G. Bulgakov 856 Integral equations with a discontinuous operatorN. V. Azbelev, R. K. Ragimkhanov, L. N. Fadeeva 862 The behavior of the integral surfaces of a homogeneous Pfaffian differential equation in the vicinity of singular raysM. V. Kozhero 874 The existence and uniqueness of the solutions of differential equations with a retardation which depends on the solution and its derivativeL. A. Zhivotovskii 880 A certain problem with a small parameterM. S. Nikol'skii 890 A partially characteristic mixed problem with Goursat initial conditions for linear equations with two-dimensional timeN. J. Yurchuk 898 Estimates of the $L_p$ norms of derivatives by a nonregular set of differential operatorsG. G. Kazaryan 911 Some model equation systems of gas dynamicsYa. I. Kanel' 922 Certain plane problems of electrostatics which are connected with the conformal mapping of circular quadranglesÈ. D. Pergamentseva 935 The interdependence of harmonic functions of different dimensionalityYu. A. Dement'ev 945 Short Communications Necessary optimality conditions for a system of integral equationsR. Gabasov 952 Certain criteria for the stability of the transformation of a locally integrable signal by a transmission systemS. T. Zavalishchin 954 On a variant of the averaging method for systems of integro-differential equationsA. N. Filatov, L. I. Talipova 958 A solution of a certain problem in control theoryN. N. Petrov 962 Isochronism in the case of a focusV. I. Chemodanov 964 Asymptotic formulae for the eigenvalues and eigenfunctions of a Sturm–Liouville type problemS. S. Krickaya 967