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 Review articles Some trends in V. Lakshmikantham's investigations in the theory of differential equations and their applicationsYu. A. Mitropol'skii, C. Lila, A. A. Martynyuk 555 Ordinary Differential Equations Necessary conditions for the preservation of smooth invariant submanifoldsI. U. Bronshtein 573 Stabilization of certain linear differential equations with second-order piecewise constant matrixB. F. Bylov, È. A. Tikhonova 581 Asymptotic behavior of solutions of a class of real-analytic systemsV. I. Varlamov 592 Boundary value problems for degenerate differential equationsN. I. Imranov 600 Generic properties of conditional exponential stability. XVV. M. Millionshchikov 607 A generalization of the fixed-point theorem and its application in a game-theoretic problem of programmed controlA. B. Pashaev 618 Stability in the large of solutions of an $n$th order equationB. N. Skachkov 624 Partial Differential Equations $L_2$-estimates for the solution of a problem for a system of equations of mixed type in a bounded domainM. A. Abdrachmanov 629 Asymptotics of the eigenvalue of a singularly perturbed selfadjoint elliptic problem with a small parameter in the boundary conditionsR. R. Gadyl'shin 640 Hyperbolically symmetrizable systems of equationsN. G. Marchuk 652 Existence and uniqueness of solutions of exterior inverse problems of potential theoryG. A. Pavlov 662 A boundary value problem for hyperbolic equations in a class of functions that are almost periodic with respect to space variablesB. I. Ptashnic, P. I. Shtabalyuk 669 Integral representations of solutions of a modified system of Euler–Poisson–Darboux equations with two lines of parabolic degenerationT. V. Chekmarev 678 Application of asymptotic estimates of Fourier transforms for finding source functions of certain elliptic systemsA. P. Chernyaev 684 An algebra of pseudodifferential operators with analytic symbolsChin' Ngok Min' 692 Short Communications Hyper–Bessel solutions of a differential equationV. S. Adamchik 697 Local boundary value problems with departure from the characteristic for the Lavrent'ev–Bitsadze equationB. U. Aubakirov, T. Sh. Kal'menov 700 Solutions of a class of third-order systemsN. S. Berezkina 702 Chaplygin's method for a system of nonlinear functional-differential equations of parabolic typeS. Bzhyhchy 705 Asymptotic representation of trajectory and period of a relaxation oscillation in case of an angular point of a separationM. I. Zharov 708 Some properties of information sets of nonlinear systemsR. Kayumov 710 A problem of stabilization of equations with aftereffectE. M. Markushin 713 Oscillations of an electromechanical systemM. D. Martynenko, N. A. Dokukova 715 A condition for the existence of the discrete spectrum of the energy operator of a system of two particles in an external fieldKh. Kh. Murtazin, A. M. Popova, V. A. Sadovnichy 717 On the behavior of a viscous compressible fluid under the action of a given boundary regimeS. M. Ponomarev 719 On the instability of difference equations with respect to the first approximationV. E. Slyusarchuk 722 A theorem on expansion with respect to the grid step of the solution of a difference problem for an abstract quasilinear hyperbolic equationL. M. Chebotareva 723 On local solvability of the Cauchy problem for equations of neutral type in the class of monotone functionsL. P. Yanovskii 728