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 The existence of a solution of a certain nonlinear boundary value problem for an $n$th-order ordinary differential equationA. Ya. Lepin, A. D. Myshkis 1171 The asymptotic properties of solutions of first order ordinary differential equationsA. V. Kostin 1184 The continuation of solutions of ordinary differential equationsS. M. Lozinskii 1196 On the question of the existence and the construction of periodic solutions of systems with lag which are close to Ljapunov systemsA. F. Kleimenov, S. N. Shimanov 1199 Accessibility of the central exponentR. È. Vinograd 1212 Local controllability of autonomous systemsN. N. Petrov 1218 Vibrations of nonautonomous systems with resonance, in the singular caseV. D. Nguyên 1233 The integrability in quadratures of certain systems of linear differential equationsA. G. Aslanyan, V. I. Burenkov 1241 An asymptotic power series expansion of the retardation of a periodic solution of an equation of neutral type with small retardationV. I. Rozhkov 1250 Certain criteria for the existence of bounded solutions of a system of differential equationsN. V. Medvedev 1258 A certain estimate of a polyharmonic function and its derivatives near the boundary of the domain. IA. S. Fokht 1265 Problems for the heat equation with mixed boundary conditionsO. Napetvaridze 1283 On the theory of multidimensional differential equations with constant coefficientsA. I. Perov 1289 A certain modified Čaplygin method for an abstract parabolic equationS. Ashirov 1299 The reduction of the fundamental boundary value problems of the theory of sloping shells to regular integral equationsS. P. Gavelya 1304 Solution of the Cauchy problem for a certain class of integro-differential equations with analytic nonlinearitiesN. A. Sidorov 1309 Convergence and estimates of error of the method of straight lines in the solution of certain problems of mathematical physicsV. N. Abrashin 1317 The Goursat problem for a second order hyperbolic equation of a special formN. J. Yurchuk 1333 Short Communications Elliptic equations in a Banach spaceP. E. Sobolevskii 1346