Recent Papers

The theory of Macdonald integrals. I. Recurrent relations. Uniformly convergent series

Solution of a completely hyperbolic equation with initial data given on a line of degeneracy

A solution is sought for an equation $$L_1L_2\dotsb L_n=f\quad(y>0),$$ which is strictly hyperbolic in a certain bounded domain $D$, where $$L_iU\equiv y^{a_i}U_{xx}-U_{yy}+a_i(x,y)U_x+b_i(x,y)U_y+c_i(x,y)U\quad(i=1,2,\dots,n),$$ satisfying the initial data $$\quad\lim_{y\to0}\frac{\partial^iU(x,y)}…

The connection between the stability of characteristic exponents and almost reducibility of systems with almost periodic coefficients

The article proves the following theorems: 1) If $A(t)$ is recurrent, then the system $\dot{x}=A(t)x$ can be reduced to the triangular form $\dot{u}=P(t)u$ with a recurrent matrix $P(t)$ by a Perron transformation $x=U(t)u$ with a recurrent matrix $U(t)$. 2) If $A(t)$ is almost periodic, then for th…

Sufficient conditions for the existence of bounded solutions of a system of differential equations

Unconditional solvability of the oblique derivative problem

Cauchy's formula and conditions of stability for the solutions of an integro-differential equation

Limit of the solution to the wave equation for an inhomogeneous medium as $t\to\infty$

The non-stationary problem \begin{equation} u_{xx}=k^2(x)u_{tt}, \tag{1} \label{1} \end{equation} is investigated, where $k(x)=k_0$ for $x<0$ and $k(x)=k_1$ for $x>x_0$, under the initial condition $u_0(x,t) = \mu(t-k_0x)$ for $t<0$, where $\mu(z)=0$ for $z<0$. It is shown that under the condition $…

The Sturm–Liouville problem of a second order nonlinear ordinary differential equation

The work is devoted to the study of the Sturm–Liouville boundary value problem \begin{equation} \begin{gathered} y''+f(t,y,y')=0,\ \alpha_{11}y(\alpha)+\alpha_{12}y'(\alpha)=0,\quad\alpha_{21}y(\beta)+\alpha_{22}y'(\beta)=0\end{gathered} \tag{1}, \end{equation}, which has been investigated by a numb…

Fundamental solutions of$B$-elliptic equations

On inverse problems of the qualitative theory of differential equations

A set of systems of differential equations is constructed, possessing specified singular points (foci, centers, nodes, and saddles), limit cycles, and separatrices. Bibliography: 5 items.

On the problem of the analytic construction of regulators

The paper considers the well-known problem of the analytical design of a controller for a linear controlled system. However, in contrast to existing developments, this study examines a more complex nonlinear case rather than a quadratic optimality criterion. For the aforementioned criterion, the pro…

Application of generalized Ljapunov functions to the investigation of non-homogeneous systems

On the question of the asymptotics of solutions to integro-differential equations with a small parameter in front of the derivative

The behavior of integral curves of a system of differential equations close to a uniform one

A group classification of the differential equations describing a one-dimensional unsteady flow of fluid

Comparison theorems for Volterra equations with retarded argument

On the averaging method in certain problems connected with averaging

Investigation of computational algorithms for the approximate integration of differential equations using the finite difference method

A general boundary value problem for elliptic systems of second order with constant coefficients. II

On the Cauchy problem, with data given on a curve of degenerate type, for a hyperbolic equation

On the solution of systems of singular integral equations with kernels invariant with respect to tranformations of a certain group

Approximate solution of a mixed boundary value problem of the theory of harmonic functions

On integrals of potential type and embedding theorems in spaces with mixed norm

On extremals

On the operational method of solution on linear differential-difference equations with constant coefficients

Estimating the limiting rate of decrease of solutions to an elliptic system

Construction of small solutions of a class of nonlinear integral equations

Mathematical consideration of certain problems on longitudinal vibrations of composite beams consisting of elastic and viscoelastic parts

Periodic solutions of a certain nonautonomous system of differential equations

A system of differential equations without moving critical singular points

Optimal control in a statistical problem

Asymptotic distribution of eigenfrequencies of a plane membrane in the case of separable variables

Resonance in a nonlinear system in the presence of random shocks

Reduction of systems of linear differential equations to the generalized$L$-diagonal form

Certain singular boundary value problems for the Bessel equation and their applications in mathematical physics

A linear periodic boundary value problem for finite differences equations

Exact estimates in the Rothe method

Certain questions of behavior of solutions of a periodic dissipative system of the second order

On the smoothness of thermal potentials. II. Thermal potentials on the surface of type$Л^{1,\alpha,\alpha/2}_{1,1,(1+\alpha)/2}$

Solution of a limiting boundary value problem for the filtration equation taking into account evaporation

On conditions of discreteness of the spectrum of monomial differential operators

On boundedness of solutions of a linear system of differential equations with variable coefficients

The jump condition in a problem of optimal control

A general boundary value problem for elliptic systems of second order with constant coefficients

Equations of neutral types with variable small retardation

A qualitative investigation of the differential equation $\frac{dy}{dx}=\frac{y+a_0x^2+a_1xy+a_2y^2}{x+b_0x^2+b_1xy+b_2y^2}$

Degenerate cases of singular integral equations with Cauchy kernel

On certain incorrect problems in the theory of potential

Approximate solution of the Wiener–Hopf equation in an exceptional case

On control over the motion of nonlinear systems