Asymptotics of solutions of discontinuous singularly perturbed boundary-value problems

We construct an asymptotic expansion of a boundary-value problem for a singularly perturbed system of differential equations with the right-hand side discontinuous at certain surface. Odessa University, Odessa. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 51, No. 6, pp. 861–864, June, 1999.     

An iteration method for the problem of averaging in the standard form

An iteration method for the enhancement of the precision of an approximate solution of the problem of averaging in the standard form is considered. Odessa University, Odessa. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 50, No. 3, pp. 426–429, March, 1998.     

Linear singularly perturbed problems with pulse influence

We establish the closeness of solutions of a linear singularly perturbed problem with asymptotically large pulse influence and the corresponding degenerate problem. Odessa University, Odessa. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 51, No. 1, pp. 133–139, January, 1999.     

Aniterative method for the solution of some singularly perturbed cauchy problems

We construct an iterative method for the solution of Cauchy problems for systems of singularly perturbed equations with fast time. Odessa University, Odessa. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 49, No. 8, pp. 1055–1060, August, 1997.     

Decomposition of systems of quasidifferential equations with rapid and slow variables

We obtain the decomposition of systems of quasidifferential equations with rapid and slow variables. Odessa University, Odessa. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 51, No. 3, pp. 413–417, March, 1999.     

On the instability of one nonautonomous essentially nonlinear equation of thenth order

We establish sufficient conditions for the Lyapunov instability of the trivial solution of a nonautonomous equation of thenth order in the case where its limit characteristic equation has a multiple zero root. The instability is determined by nonlinear terms. Odessa University, Odessa. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 51, No. 6, pp. 835–841, June, 1999.     

Nonsymmetric problem of divisors in an arithmetic progression

We investigate the distribution of values of a nonsymmetric divisor functiond(a,b; n) in an arithmetic progression with increasing difference. Odessa University, Odessa. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 51, No. 6, pp. 753–761, June, 1999.     

Functional polystability of some nonautonomous quasilinear differential systems

For quasilinear differential systems with a boundary matrix of coefficients of the system of the first approximation, we obtain sufficient conditions of functional polystability, which generalizes the notion of exponential polystability. Odessa University, Odessa. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 51, No. 7, pp. 989–995, July, 1999.     

On the analyticity of the Fourier original and Fourier transform inside alternate angles

We prove that a Fourier image is an analytic function inside two alternate angles if the Fourier preimage possesses the same property. Odessa Academy of Building and Architecture, Odessa. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 51, No. 5, pp. 703–707, May, 1999.     

Mean oscillations and the convergence of Poisson integrals

We establish conditions for mean oscillations of a periodic summable function under which the summability of its Fourier series (conjugate series) by the Abel-Poisson method at a given point implies the convergence of Steklov means (the existence of the conjugate function) at the indicated point. Similar results are also obtained for the Poisson integral in ℝ ₊ⁿ⁺¹. Odessa University, Odessa. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 49, No. 2, pp. 206–222, February, 1997.     

Infinite hankel matrices and generalized carathéodory — fejer and riesz problems

Sans résuméPedagogical Institute, Odessa, and Odessa Engineering Construction Institute. Translated from Funktsional'nyi Analiz i Ego Prilozheniya, Vol. 2, No. 1, pp. 1–19, January–March, 1968.     

On asymptotic decompositions of o-solutions in the theory of quasilinear systems of difference equations

We consider a quasilinear system of difference equations with certain conditions. We prove that there exists a formal partial o-solution of this system in the form of functional series of special type. We also prove a theorem on the asymptotic behavior of this solution. Odessa University, Odessa. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 49, No. 5, pp. 672–677, May, 1997.     

Critical cases of stability of one nonautonomous essentially nonlinear equation of the nth order

We establish sufficient conditions of the Lyapunov stability of the trivial solution of a nonautonomous ordinary differential equation of the nth order in the case where its characteristic equation has a multiple zero root. The stability is determined by nonlinear terms. Odessa University, Odessa. Translated from Ukrainskii Matematicheskii, Zhurnal, Vol. 49, No. 5, pp. 720–724, May, 1997.     

Asymptotics of solutions of a second-order linear differential system with a special right-hand side

Odessa. Translated from Sibirskii Matematicheskii Zhurnal, Vol. 31, No. 2, pp. 89–93, March–April, 1990.     

On the discrete spectrum of a boundary value problem

Odessa. Translated from Sibirskii Matematicheskii Zhurnal, Vol. 31, No. 5, pp. 182–186, September–October, 1990.     

A problem of control of bundles of trajectories

Odessa. Translated from Sibirskii Matematicheskii Zhurnal, Vol. 33, No. 2, pp. 196–199, March–April, 1992.     

Eigenvalues of a certain quadratic pencil of operators

Odessa Construction Engineering Institute. Translated from Funktsional'nyi Analiz i Ego Prilozheniya, Vol. 23, No. 1, pp. 80–81, January–March, 1989.     

On a certain boundary value problem of N. P. Vekua with a piecewise-smooth shift on a piecewise Lyapunov contour

Odessa. Translated from Sibirskii Matematicheskii Zhurnal, Vol. 33, No. 2, pp. 108–115, March–April, 1992.     

A singular case of the problem of absolute stability of systems with lag (and scalar control)

Odessa. Translated from Sibirskii Mathematicheskii Zhurnal, Vol. 32, No. 5, pp. 112–125, September–October, 1991.     

Optimal passive systems and semiboundedness of quadratic functionals

Odessa. Translated from Sibirskii Matematicheskii Zhurnal, Vol. 33, No. 1, pp. 78–86, January–February, 1992.