Review articles


Some trends in V. Lakshmikantham's investigations in the theory of differential equations and their applications Yu. A. Mitropol'skii, C. Lila, A. A. Martynyuk

555 

Ordinary Differential Equations


Necessary conditions for the preservation of smooth invariant submanifolds I. U. Bronshtein

573 

Stabilization of certain linear differential equations with secondorder piecewise constant matrix B. F. Bylov, È. A. Tikhonova

581 

Asymptotic behavior of solutions of a class of realanalytic systems V. I. Varlamov

592 

Boundary value problems for degenerate differential equations N. I. Imranov

600 

Generic properties of conditional exponential stability. XV V. M. Millionshchikov

607 

A generalization of the fixedpoint theorem and its application in a gametheoretic problem of programmed control A. B. Pashaev

618 

Stability in the large of solutions of an $n$th order equation B. 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 domain M. A. Abdrachmanov

629 

Asymptotics of the eigenvalue of a singularly perturbed selfadjoint elliptic problem with a small parameter in the boundary conditions R. R. Gadyl'shin

640 

Hyperbolically symmetrizable systems of equations N. G. Marchuk

652 

Existence and uniqueness of solutions of exterior inverse problems of potential theory G. A. Pavlov

662 

A boundary value problem for hyperbolic equations in a class of functions that are almost periodic with respect to space variables B. I. Ptashnic, P. I. Shtabalyuk

669 

Integral representations of solutions of a modified system of Euler–Poisson–Darboux equations with two lines of parabolic degeneration T. V. Chekmarev

678 

Application of asymptotic estimates of Fourier transforms for finding source functions of certain elliptic systems A. P. Chernyaev

684 

An algebra of pseudodifferential operators with analytic symbols Chin' Ngok Min'

692 

Short Communications


Hyper–Bessel solutions of a differential equation V. S. Adamchik

697 

Local boundary value problems with departure from the characteristic for the Lavrent'ev–Bitsadze equation B. U. Aubakirov, T. Sh. Kal'menov

700 

Solutions of a class of thirdorder systems N. S. Berezkina

702 

Chaplygin's method for a system of nonlinear functionaldifferential equations of parabolic type S. Bzhyhchy

705 

Asymptotic representation of trajectory and period of a relaxation oscillation in case of an angular point of a separation M. I. Zharov

708 

Some properties of information sets of nonlinear systems R. Kayumov

710 

A problem of stabilization of equations with aftereffect E. M. Markushin

713 

Oscillations of an electromechanical system M. 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 field Kh. Kh. Murtazin, A. M. Popova, V. A. Sadovnichy

717 

On the behavior of a viscous compressible fluid under the action of a given boundary regime S. M. Ponomarev

719 

On the instability of difference equations with respect to the first approximation V. 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 equation L. M. Chebotareva

723 

On local solvability of the Cauchy problem for equations of neutral type in the class of monotone functions L. P. Yanovskii

728 