Preamble

DIFFERENTIAL EQUATIONS, JULY 1965, VOLUME I, NO. 7

This section presents a bibliography of recent Soviet research in the field of differential equations and related mathematical methods, published in early 1965.

Gordeziani, D. G. "On the numerical solution of a quasilinear parabolic equation." Soobshch. AN Gruz. SSR [Communications of the Academy of Sciences of the Georgian SSR], 1965, No. 1, 37, pp. 3–10. (Summary in Georgian).

Gokhberg, I. Ts., and Feldman, I. A. "On the approximate solution of certain classes of linear equations." DAN SSSR [Doklady Akademii Nauk SSSR], 1965, No. 4, pp. 750–753.

Gredzhuk, I. F. "On a method for estimating the solution of the Cauchy problem for an $n$-th order linear differential equation." DAN USSR [Doklady Akademii Nauk Ukrainskoy SSR], 1965, No. 1, pp. 10–14.

Gribanov, Yu. I. "On the projection method for solving linear equations in Banach spaces." Izv. vyssh. ucheb. zavedeniy. Matematika [News of Higher Educational Institutions. Mathematics], 1965, No. 1, pp. 48–55.

Grudo, E. I. "On the analytical theory of systems of linear differential equations with an irregular singular point." Differents. uravneniya [Differential Equations], 1965, Vol. I, No. 3, pp. 318–326.

Grudo, E. I. "On a case of the Volterra integral equation." Differents. uravneniya, 1965, Vol. I, No. 2, pp. 214–218.

Daugavet, I. K. "On the method of moments for ordinary differential equations." Sibir. matem. zh. [Siberian Mathematical Journal], 1965, No. 1, pp. 70–85.

Demidovich, B. P. "On a generalization of the Lyapunov stability criterion for regular systems." Matem. sb. [Mathematical Collection], 1965, No. 3, pp. 344–353.

Dzhavadov, M. G. "Asymptotics of the solution to a boundary value problem for a second-order elliptic equation in domains where one dimension is sufficiently small compared to others." DAN SSSR, 1965, No. 3, pp. 507–510.

Dzhavadov, M. G. "On the $m$-fold completeness of half of the eigenfunctions and associated functions of a $2n$-th order ordinary differential operator." DAN SSSR, 1965, No. 4, pp. 754–757.

Dmitriev, V. I. "Diffraction of a plane electromagnetic field by cylindrical bodies located in layered media." In Vychislitel'nye metody i programmirovanie [Computational Methods and Programming], III. Moscow: Moscow University Press, 1965, pp. 307–316.

Dobryakov, L. D., and Kantor, I. L. "On the solution of a system of inconsistent linear equations in the Chebyshev sense." Sibir. matem. zh., 1965, No. 1, pp. 238–240.

Dubnov, V. L. "On the existence and uniqueness 'in the large' of the solution to the Hamilton–Jacobi equation." Vestn. Mosk. un-ta. Seriya I. Matem., mekhan. [Bulletin of Moscow University. Series I. Mathematics, Mechanics], 1965, No. 2, pp. 3–9.

Dyakonov, E. G. "On some iterative methods for solving systems of difference equations arising from the grid method for elliptic partial differential equations." In Vychislitel'nye metody i programmirovanie, III, Moscow University Press, 1965, pp. 191–222. (26 refs.)

Dyakonov, E. G. "Second-order accurate difference schemes with a splitting operator for multidimensional parabolic equations with variable coefficients." In Vychislitel'nye metody i programmirovanie, III, Moscow University Press, 1965, pp. 163–190. (33 refs.)

Erugin, A. N. "Analytical structure and basic properties of solutions to equations with algebroid right-hand sides in the case of a focus and generalizations." Differents. uravneniya, 1965, Vol. 1, No. 3, pp. 303–312.

Erugin, A. N. "Analytical structure of solutions to certain differential equations with a right-hand side that is non-periodic with respect to the argument." DAN BSSR [Doklady Akademii Nauk BSSR], 1965, 9, No. 1, pp. 7–10.

Zhautykov, O. A. "Countable systems of differential equations and their applications." Differents. uravneniya, 1965, Vol. I, No. 2, pp. 162–170. (14 refs.)

Zadiraka, K. V. "On a non-local integral manifold of an irregularly perturbed differential system." Ukr. matem. zh. [Ukrainian Mathematical Journal], 1965, 17, No. 1.

Ivanov, V. K. "The Cauchy problem for the Laplace equation in an infinite strip." Differents. uravneniya, 1965, Vol. I, No. 1.

Ivanov, V. K. "On the existence of the fundamental function of a linear differential operator with constant coefficients under periodicity conditions." Izv. vyssh. ucheb. zavedeniy. Matematika, 1965, No. 1, pp. 62–67.

Ivanov, E. A., and Ilyukevich, S. F. "Diffraction of a plane electromagnetic wave by two pairs of parallel coaxial cylinders." Differents. uravneniya, 1965, Vol. I, No. 1, pp. 117–130.

Ivanov, E. A., and Ilyukevich, S. F. "On the diffraction of a plane electromagnetic wave by a grating of coaxial cylinders." Differents. uravneniya, 1965.

Ivanov, E. A. "Third All-Union Symposium on Wave Diffraction." Differents. uravneniya, 1965, Vol. I, No. 2, pp. 275–280.

Inozemtseva, I. N. "A theorem on the sign of the Green's function for a fifth-order linear differential equation." Izv. vyssh. ucheb. zavedeniy. Matematika, 1965, No. 1.

Karaseva, T. M. "On the growth rate and boundedness of solutions to second-order differential equations with periodic coefficients." Izv. AN SSSR, ser. matem. [Bulletin of the Academy of Sciences of the USSR, Mathematics Series], 1965, pp. 41–70.

Karpilovskaya, E. B. "On the convergence of the subdomain method for ordinary integro-differential equations." Zh. vychisl. matematiki i matem. fiziki [Journal of Computational Mathematics and Mathematical Physics], 1965, No. 1.

Kiguradze, I. T. "On the Cauchy problem for ordinary differential equations with a singularity." Soobshch. AN Gruz. SSR, 1965, 37, No. 1, pp. 19–24. (Summary in Georgian).

Kovach, Yu. I. "Approximate integration of the Cauchy problem for a $2n$-th order quasilinear hyperbolic differential equation using the S. A. Chaplygin method." DAN USSR, 1965, pp. 27–30.

Kovach, Yu. I. "Application of the theorem on differential inequalities to the Goursat problem for a linear system of partial differential equations." Differents. uravneniya, 1965, Vol. I, No. 3, pp. 411–420.

Kozlov, E. M. "On an improper integral in operational calculus." DAN USSR, 1965, No. 3, pp. 263–265. (In Ukrainian).

Kordzadze, R. A. "On singular integral equations with a shift." DAN SSSR, 1965, 160, No. 6, pp. 1242–1243.

Kocheva, M. D. "On the circular motions of a double pendulum." Differents. uravneniya, 1965, No. 2, pp. 187–195.

Kocheva, M. D. "On the oscillations of a double pendulum." Differents. uravneniya, 1965, Vol. I, No. 3, pp. 374–386.

Kravchenko, T. K., and Yablonsky, A. I. "Solution of an infinite boundary value problem for a third-order equation." Differents. uravneniya, 1965, Vol. I, No. 3, pp. 327–329.

Krasovsky, N. N. "On the stabilization of dynamical systems by additional forces." Differents. uravneniya, 1965, Vol. I, No. 1, pp. 5–16.

Krasovsky, N. N. "On a property of a linear stable system fully controllable under random action." Differents. uravneniya, 1965, Vol. I, No. 2, pp. 143–156.

Kudaev, M. B. "Classification of multidimensional systems of ordinary differential equations using Lyapunov functions." Differents. uravneniya, 1965, Vol. I, pp. 346–356. (11 refs.)

Kuzhel, A. V. "On the spectrum of a non-self-adjoint Sturm–Liouville differential operator on a semi-axis." DAN USSR, 1965, No. 2, pp. 157–160.

Kuznetsov, N. N., and Rozhdestvensky, B. L. "On the construction of a generalized solution to the Cauchy problem for a quasilinear equation." Uspekhi matem. nauk [Successes in Mathematical Sciences], 1965, pp. 209–212.

Kurzhansky, A. B. "On the calculation of optimal control in a system with incomplete information." Differents. uravneniya, 1965, Vol. I, No. 3, pp. 360–373. (13 refs.)

Kurzhansky, A. B. "On the analytical design of a regulator in a system with noise depending on the control." Differents. uravneniya, 1965, Vol. I, No. 2, pp. 204–213.

Lavrentyev, M. M. "On a class of inverse problems for differential equations." DAN SSSR, 1965, 160, No. 1, pp. 32–35.

Latipov, Kh. R. "On the distribution of singular points of Frommer's equation on the entire plane." Izv. vyssh. ucheb. zavedeniy. Matematika, 1965, No. 1, pp. 96–104.

Lebedev, V. I., and Dyakonov, E. G. "On the application of difference schemes with a splitting operator for solving the third boundary value problem for parabolic equations." Sibir. matem. zh., 1965, No. 1, pp. 108–113.

Leonov, V. V. "Topological properties of the solution to a system of nonlinear differential equations in the neighborhood of a movable singular point." Sibir. matem. zh., 1965, No. 1.

Li Mun Su. "On the existence and continuability of the solution to a system of Volterra integral equations whose right-hand side is a discontinuous operator." Differents. uravneniya, 1965, Vol. I, No. 3, pp. 387–392.

Lidsky, E. A. "On the stability of motion of a system with random delays." Differents. uravneniya, 1965, Vol. I, No. 1.

Liskovets, O. A. "The method of hyperplanes in non-stationary problems with a self-adjoint operator." Differents. uravneniya, 1965, Vol. I, No. 2, pp. 255–259.

Littman, W., Stampacchia, G., and Weinberger, H. F. "Regular points for elliptic equations with discontinuous coefficients." Translated by G. Maz'ya. Matematika. Sb. perevodov [Mathematics. Collection of Translations], 1965, 9:2, pp. 72–97. (31 refs.)

Logunov, A. I., and Tsalyuk, Z. B. "On the uniqueness of solutions to Volterra integral equations with a lagging argument." DAN SSSR, 1965.

Lukashevich, N. A. "Isochronism of the center of certain systems of differential equations." Differents. uravneniya, 1965, Vol. I, No. 3, pp. 295–302. (13 refs.)

Lukashevich, N. A. "Integral curves of a certain differential equation." Differents. uravneniya, 1965, Vol. I, No. 1, pp. 82–95.

Lukashevich, N. A. "On the stability of the trivial solution of a system of differential equations." Differents. uravneniya, 1965, Vol. I, No. 2, pp. 196–198.

Lunkevich, V. A., and Sibirsky, K. S. "On the conditions for a center." Differents. uravneniya, 1965, Vol. I, No. 2.

Melamed, V. B. "On formal solutions of certain nonlinear equations." Sibir. matem. zh., 1965, No. 1, pp. 165–177.

Millionshchikov, V. M. "Recurrent and almost periodic limit trajectories of non-autonomous systems of differential equations." DAN SSSR, 1965.

Nazarov, E. A. "Methods for approximating trajectories of a system of three differential equations with non-analytical right-hand sides to a limit cycle." Differents. uravneniya, 1965, Vol. I, No. 3, pp. 313–317.

Olevsky, M. N. "On the connections between solutions of the singular Cauchy problem related to the generalized Euler–Poisson–Darboux differential-operator equation." DAN SSSR, 1965, No. 5, pp. 1009–1012.

Panich, O. I. "On the solvability of exterior boundary value problems for the wave equation and for the system of Maxwell equations." Uspekhi matem. nauk, 1965, 20, No. 1.

Pliss, V. A. "On the reduction of an analytical system of differential equations to linear form." Differents. uravneniya, 1965, Vol. I, No. 2.

Pliss, V. A. "On the existence of a family of periodic solutions for a system of differential equations in the case of zero roots." Differents. uravneniya, 1965, Vol. I, No. 1, pp. 17–24.

Prikazchikov, V. G. "Homogeneous fourth-order accurate difference schemes for the Sturm–Liouville problem." In Vychislitel'nye metody i programmirovanie, Moscow University Press, 1965, pp. 232–236.

Rakovshchik, L. S. "On a convolution-type integral equation." Sibir. matem. zh., 1965, No. 1, pp. 186–198.

Ramm, A. G. "Spectral properties of the Schrödinger operator in domains with an infinite boundary." Matem. sb., 1965, No. 3, pp. 321–343.

Rudakov, V. P. "On the existence of an interval of stability of motion based on the first approximation." Differents. uravneniya, 1965, Vol. I, No. 3, pp. 357–359.

Ruzmetov, E. "On a generalization of V. Pogorzhelsky's theorem and the applicability of the method of successive approximations to multidimensional nonlinear singular integral equations." DAN Tadzhik. SSR [Doklady Akademii Nauk Tadzhikskoy SSR], 1965, 8, No. 1, pp. 7–11. (Summary in Tajik).

Sagitov, M. S., and Filatov, A. N. "On Lyapunov stability in the critical case when the characteristic equation has an even number of zero roots." PMM [Applied Mathematics and Mechanics], 1965, 29, No. 1, pp. 173–175.

Samarsky, A. A., and Mostinskaya, S. B. "Numerical solution of the two-dimensional heat equation with discontinuous coefficients in polar coordinates." In Vychislitel'nye metody i programmirovanie, III, Moscow University Press, 1965, pp. 147–162. (10 refs.)

(To be continued in No. 8)

Compiled by A. R. Shakun.
Submitted for typesetting: May 26, 1965. Approved for printing: July 19, 1965.
Published by "Nauka i Tekhnika" of the Academy of Sciences of the BSSR, Minsk.