Preamble

DIFFERENTIAL EQUATIONS, JUNE 1966, VOLUME II, NO. 6

Ordinary Differential Equations

Abgaryan, K. A. Asymptotic splitting of equations for a linear automatic control system. Dokl. Akad. Nauk SSSR, 1966, Vol. 166, No. 2, pp. 301–304. (10 refs.)

Abutaliev, F. B., and Vilenchik, V. B. Chaplygin’s vortex equation. Vopr. Vychisl. Mat. Tekh. (Institute of Mechanics and Computing Center, Academy of Sciences of the Uzbek SSR), 1965, Iss. 7.

Aizengendler, P. G., and Vainberg, M. M. On periodic solutions of non-autonomous systems. Dokl. Akad. Nauk SSSR, 1965, Vol. 165, No. 2, pp. 255–257. (7 refs.)

Allan M. Krall. On non-self-adjoint ordinary differential operators of the second order. Dokl. Akad. Nauk SSSR, 1965, Vol. 165, No. 6, pp. 1235–1237. (7 refs.)

Albrecht, E. G. On the existence of an optimal Lyapunov function and continuous optimal control for a problem of analytical regulator construction. Differ. Uravn., 1965, Vol. 1, No. 10, pp. 1301–1311. (25 refs.)

Anarbaev, U. On the solution of the differential equation $y'' + (ax)y = 0$. Vopr. Vychisl. Mat. Tekh. (Institute of Mechanics and Computing Center, Academy of Sciences of the Uzbek SSR), 1965, Iss. 7, pp. 27–34.

Anarson, S. Kh. Systems of the first degree of non-roughness on a torus. Dokl. Akad. Nauk SSSR, 1965, Vol. 164, No. 5, pp. 959–962. (8 refs.)

Beiko, I. V. A numerical method for solving the problem of optimal pursuit based on time maximin. Ukr. Mat. Zh., 1966, Vol. 18, No. 1, pp. 104–106.

Blashchak, V. A. On a second-order differential operator on the entire axis with spectral singularities. Dokl. Akad. Nauk UkrSSR, 1966, No. 1. (6 refs. In Ukrainian.)

Blinchevsky, V. S. On the construction of a zero approximation when solving the Cauchy problem for a system of ordinary differential equations using the S. A. Chaplygin method. Differ. Uravn., 1965, Vol. 1, No. 11, pp. 1544–1547.

Blyumkina, I. A. On the solution of a boundary value problem for a Chaplygin-type equation with data on a parabolic line and characteristic. Vestn. Leningr. Univ. Mat. Mekh. Astron., 1966, No. 1, Iss. 1, pp. 107–119. (7 refs.)

Borisov, A. P. Questions on the number of limit cycles arising in systems of differential equations with discontinuous right-hand sides. Vestn. Mosk. Univ. Mat. Mekh., 1966, No. 1. (6 refs.)

Boyarchuk, A. K. KO-stability of conservative difference schemes for a fourth-order differential equation and system of differential equations with discontinuous coefficients. Differ. Uravn., 1965, Vol. 1, No. 12, pp. 1652–1661.

Boyarchuk, A. K. On difference schemes for a fourth-order differential equation with discontinuous coefficients. Vychisl. Mat., 1965, Iss. 1, pp. 107–115. (5 refs.)

Breus, K. A. Canonical systems of differential equations with rapidly varying periodic coefficients. Ukr. Mat. Zh., 1966, Vol. 18, No. 1, pp. 3–10.

Brushlinskaya, N. N. On a method for proving the convergence of formal solutions for certain nonlinear equations. Vestn. Mosk. Univ. Mat. Mekh., 1965, No. 6, pp. 3–7. (7 refs.)

Bryuno, A. D. On the convergence of transformations of differential equations to normal form. Dokl. Akad. Nauk SSSR, 1965, No. 5, pp. 987–989. (9 refs.)

Bulgakov, N. G., and Krasovsky, N. N. On the stabilization of non-stationary systems. PMM (Prikl. Mat. Mekh.), 1965, Vol. 29, Iss. 6, pp. 1081–1083. (8 refs.)

Burd, V. Sh. Parameter dependence of almost periodic solutions of differential equations with deviating argument. Dokl. Akad. Nauk AzSSR, 1965, Vol. 21, No. 5, pp. 3–7. (7 refs.)

Buriev, T. Solving a system of ordinary linear second-order differential equations by Taylor series expansion on a computer. Vopr. Vychisl. Mat. Tekh. (Institute of Mechanics and Computing Center, Academy of Sciences of the Uzbek SSR), 1965, Iss. 7, pp. 59–67. (6 refs.)

Butkovsky, A. G., and Poltavsky, L. N. Optimal control of a distributed oscillatory system. Avtom. Telemekh., 1965, Vol. 26, No. 11, pp. 1900–1914.

Bykov, Ya. V. On a class of systems of ordinary differential equations. Differ. Uravn., 1965, Vol. 1, No. 11, pp. 1449–1476. (13 refs.)

Bylov, B. F. Generalization of Perron's theorem [1]. Differ. Uravn., 1965, Vol. 1, No. 12, pp. 1597–1600.

Vishik, M. I., and Eskin, G. I. Convolution equations in a bounded domain in spaces with weighted norms. Mat. Sb., 1966, Vol. 69, Iss. 1, pp. 65–110. (10 refs.)

Volin, M., and Ostrovsky, G. M. On the optimization of a continuous production process described by systems of ordinary differential equations. Izv. Akad. Nauk SSSR, Tekhn. Kibern., 1965, No. 5, pp. 137–142.

Volosov, V. M., Medvedev, G. N., and Morgunov, B. I. Application of the averaging method to the calculation of certain systems of differential equations with deviating argument. Vestn. Mosk. Univ. Fiz. Astron., 1965, No. 6. (8 refs.)

Galperin, E. A. On the stabilization of steady-state motions of a nonlinear controlled system in the critical case of a pair of purely imaginary roots. PMM, 1965, Vol. 29, Iss. 6, pp. 1070–1080. (9 refs.)

Gerashchenko, E. I., and Kiselev, L. V. On the stability of a control system with a forced sliding mode. Differ. Uravn., 1965, Vol. 1, No. 12.

Gerashchenko, E. I., and Kleimenov, A. F. Analysis of a nonlinear system by the method of separation of motions. Differ. Uravn., 1965, Vol. 1, No. 10, pp. 1292–1300.

Gikhman, I. I., and Dorogovtsev, A. Ya. On the stability of solutions of stochastic differential equations. Ukr. Mat. Zh., 1965, Vol. 17, No. 6, pp. 3–21. (8 refs.)

Gorsky, V. B. Construction of a shock-free nozzle with weak discontinuities. Izv. Vyssh. Uchebn. Zaved. Mat., 1965, No. 6, pp. 63–66.

Grobman, D. M. Analogy of systems of differential equations near a singular point. Dokl. Akad. Nauk SSSR, 1966, Vol. 166, No. 1, pp. 15–18. (5 refs.)

Daletsky, Yu. L., and Kukharchuk, N. M. First-order equations with functional derivatives. Ukr. Mat. Zh., 1965, Vol. 17, No. 6, pp. 114–117.

Derendyaev, I. M. Approximate construction of admissible controls. Izv. Vyssh. Uchebn. Zaved. Mat., 1966, No. 1.

Dragilev, A. V. A theorem and problem from the qualitative theory of differential equations. Differ. Uravn., 1965, Vol. 1, No. 12, pp. 1679–1681. (5 refs.)

Evgrafov, M. A., and Fedoryuk, M. V. Asymptotics of solutions to the equation $w''(z) - p(z, \lambda) \lambda w(z) = 0$ as $\lambda \to \infty$ in the complex plane. Usp. Mat. Nauk, 1966, Vol. 21, Iss. 1, pp. 3–50. (34 refs.)

Egorov, A. I. Optimal processes in systems with distributed parameters and some problems in invariance theory. Izv. Akad. Nauk SSSR Ser. Mat., 1965, Vol. 29, No. 6, pp. 1205–1260. (40 refs.)

Egorov, V. G. Singular points of systems of equations in total differentials. Ukr. Mat. Zh., 1965, Vol. 17, No. 6, pp. 117–122.

Erugin, A. N. Analytical structure of the solution to equation (2.1). Differ. Uravn., 1965, Vol. 1, No. 12, pp. 1606–1619. (7 refs.)

Zhikov, V. V. Almost-periodic solutions of differential equations in Hilbert space. Dokl. Akad. Nauk SSSR, 1965, Vol. 165, No. 6, pp. 1227–1230. (8 refs.)

Zhukovsky, V. I. Instability and conditional stability in the critical case of zero roots. Differ. Uravn., 1965, Vol. 1, No. 12. (5 refs.)

Zeynalova, A. A. On the completeness of the system of eigenfunctions and associated functions of a non-self-adjoint differential operator generated by a differential expression with a delayed argument. In: Some Questions of Functional Analysis and Its Applications. Baku: Akad. Nauk AzSSR, 1965.

Zelenyak, T. I. On stationary solutions of mixed problems arising in the study of certain chemical processes. Differ. Uravn., 1966, pp. 205–213. (5 refs.)

Ivanov, V. N. On linear differential operators in spaces of almost-periodic functions. Tr. Sarat. Inst. Mekhan. Selsk. Khoz., 1965, Iss. 38. (6 refs.)

Ilyin, A. A. On the question of finding limit cycles for an autonomous system of differential equations. Izv. Vyssh. Uchebn. Zaved. Mat., 1966, No. 1.

Kabulov, R. On the solvability of a fractional-power solution of the Cauchy problem for a class of equations in Banach space (rank equals one). Izv. Akad. Nauk UzSSR Ser. Fiz.-Mat. Nauk, 1965, No. 6. (6 refs.)

Kalinin, S. V. On the stability of motion of an object equipped with an automatic control device. Vestn. Mosk. Univ. Mat. Mekh., 1965, No. 6, pp. 64–69. (8 refs.)

Kamenkov, G. V. On the stability of motion in critical cases. PMM, 1965, Vol. 29, Iss. 6, pp. 1053–1069. (8 refs.)

Kiguradze, I. T. A comparison lemma and the question of uniqueness of the solution to a problem for ordinary differential equations. Soobshch. Akad. Nauk GruzSSR, 1965, Vol. 39, No. 3, pp. 513–518. (8 refs.)

Kiguradze, I. T. On the Cauchy problem for singular systems of ordinary differential equations. Differ. Uravn., 1965, Vol. 1, No. 10, pp. 1271–1291. (6 refs.)

Kiguradze, I. T. A note on the boundedness of solutions of differential equations. Tr. Tbilis. Univ., 1965, Vol. 110, pp. 103–108.

Kirillova, L. S. The general problem of terminal control in linear systems. Avtom. Telemekh., 1965, Vol. 26, No. 12, pp. 2120–2130.

Komarenko, N., Lukovsky, I., and Feshchenko, S. F. On the eigenvalue problem with a parameter in the boundary conditions. Ukr. Mat. Zh., 1965, Vol. 17, No. 6, pp. 22–30. (7 refs.)

Komarnitskaya, O. I. Stability of controlled systems taking into account the external load of a hydraulic servomotor. Avtom. Telemekh., 1965, Vol. 26, No. 7, pp. 1205–1210.

Komlenko, Yu. V. On some estimates of the interval of applicability of S. A. Chaplygin's theorem on differential inequalities and stability criteria for differential equations with periodic coefficients. Izv. Vyssh. Uchebn. Zaved. Mat., 1966, No. 1, pp. 99–103. (5 refs.)

Korobeinik, Yu. F. On the Cauchy problem for a linear differential equation of infinite order. Litov. Mat. Sb., 1965, Vol. 5, No. 3, pp. 397–420. (13 refs.)

Kotov, E. O. Toward the analysis of linear systems with variable parameters. Avtom. Telemekh., 1965, Vol. 26, No. 12, pp. 2113–2119. (5 refs.)

Kochetkov, Yu. A. Application of the Pontryagin method to the study of minimax problems in control processes. Izv. Akad. Nauk SSSR, Tekhn. Kibern., 1965, No. 5, pp. 13–22. (5 refs.)

Krasovsky, N. N. The problem of observing a linear dynamic system and equations with a delayed argument. Differ. Uravn., 1965, Vol. 1, No. 12. (6 refs.)

Krasovsky, N. N. On optimal control with discrete feedback signals. Differ. Uravn., 1965, Vol. 1, No. 11, pp. 1415–1427. (10 refs.)

Krasnoselsky, M., Levin, Yu., and Mamedov, Ya. D. On estimates of solutions of second-order differential equations. Ukr. Mat. Zh., 1966, Vol. 18, No. 1, pp. 110–116. (6 refs.)

Lavrentyev, I. M. On an existence theorem for differential equations with a discontinuous right-hand side. Differ. Uravn., 1965, Vol. 1, No. 11, pp. 1477–1481.

Laricheva, V. V. Effective transformation and asymptotics of a class of nonlinear differential equations. Dokl. Akad. Nauk SSSR, 1965, Vol. 165, No. 2, pp. 289–292.

Levitan, B. M., and Sargsyan, I. S. On the extension of solutions of a one-dimensional Dirac system. Dokl. Akad. Nauk SSSR, 1965, Vol. 165, No. 6, pp. 1241–1244.

Lifshits, E. A. On duality principles for the problem of periodic solutions of higher-order differential equations. Dokl. Akad. Nauk SSSR, 1965, Vol. 165, No. 2, pp. 277–280. (7 refs.)

Lunkevich, V., and Sibirsky, K. S. Center conditions for homogeneous nonlinearities of the third degree. Differ. Uravn., 1965, Vol. 1, No. 11, pp. 1482–1487. (12 refs.)

Malkin, K. E. Center conditions for a class of differential equations. Izv. Vyssh. Uchebn. Zaved. Mat., 1966, No. 1, pp. 104–114. (16 refs.)

Malyshev, Yu. V. Investigation of differential equations close to homogeneous ones. Vestn. Mosk. Univ. Mat. Mekh., 1965, No. 6, pp. 15–27.

Mamedov, Ya. D. The limit Cauchy problem for first and second-order differential equations with unbounded nonlinear potential operators. Dokl. Akad. Nauk SSSR, 1965, Vol. 164, No. 6, pp. 1239–1242.

Mamedov, Ya. D. One-sided estimates in conditions of asymptotic stability of solutions of differential equations with unbounded operators. Dokl. Akad. Nauk SSSR, 1966, Vol. 166, No. 3, pp. 533–535. (5 refs.)

Martynov, V. V. Conditions for discreteness and continuity of the spectrum in the case of a self-adjoint system of first-order differential equations. Dokl. Akad. Nauk SSSR, 1965, Vol. 165, No. 5, pp. 996–999.

Martynov, V. V. Conditions for discreteness and continuity of the spectrum in the case of a self-adjoint system of even-order differential equations. Differ. Uravn., 1965, Vol. 1, No. 12, pp. 1578–1591.

Maslov, V. P. Asymptotics of the eigenvalues of the Schrödinger operator. Usp. Mat. Nauk, 1965, Vol. 20, Iss. 6, pp. 134–138.

Masko, E. S., and Ostrovsky, G. M. On the calculation of optimal systems. Avtom. Telemekh., 1965, Vol. 26, No. 12, pp. 2131–2136.

Matveev, R. F. On the asymptotics of the solution to a system of linear differential equations with small random coefficients. Teor. Veroyatn. Primen., 1965, Vol. 10, Iss. 3, pp. 567–570.

Medvedev, N. V. On bounded solutions of a system of differential equations. Differ. Uravn., 1965, Vol. 1, No. 12, pp. 1592–1596.

Millionshchikov, V. M. On the stability of characteristic exponents of limit solutions of linear systems. Dokl. Akad. Nauk SSSR, 1966, Vol. 166, No. 1, pp. 34–37. (14 refs.)

Milshtein, G. N. On a boundary value problem for a system of two differential equations. Differ. Uravn., 1965, Vol. 1, No. 12, pp. 1628–1639. (11 refs.)

Mitropolsky, Yu. A., and Samoilenko, A. M. On the construction of solutions of linear differential equations with quasi-periodic coefficients using the method of accelerated convergence. Ukr. Mat. Zh., 1965, Vol. 17, No. 6, pp. 42–59. (12 refs.)

Mosolov, P. P. On a boundary value problem for symmetric differential operators. Vestn. Mosk. Univ. Mat. Mekh., 1966, No. 1, pp. 64–69.

Myshkis, A. D., and Egle, I. Yu. Generalization of the conditions of complete integrability for the Pfaffian equation. Izv. Akad. Nauk LatvSSR Ser. Fiz. Tekh. Nauk, 1965, No. 4, pp. 41–52.

Nelepin, R. A. On the investigation of systems with two nonlinear elements by exact methods. Izv. Vyssh. Uchebn. Zaved. Radiofiz., 1965, Vol. 8, No. 3, pp. 579–588.

Oleinikov, V. A. On the transcendence and algebraic independence of $E$-functions that are solutions to a third-order linear differential equation. Dokl. Akad. Nauk SSSR, 1966, Vol. 166, No. 3, pp. 540–543.

Orkina, E. L. Application of discontinuous Lyapunov functions for the stability analysis of nonlinear tracking systems. Avtom. Telemekh., 1965, Vol. 26, No. 12.

Pavlov, V. V. General questions of invariance and autonomy in essentially nonlinear systems. Avtomatika, 1965, No. 2, pp. 79–80.

Paraev, Yu. I. On optimal control processes with stochastic feedback. Avtom. Telemekh., 1965, Vol. 26, No. 10, pp. 1672–1681. (10 refs.)

Peretyagin, M. On the number of limit cycles of the equation $dy/dx = P(x, y)/Q(x, y)$, where $P$ and $Q$ are polynomials. Uch. Zap. Smolensk. Ped. Inst., 1965, Vol. 1, Iss. 14.

Perov, A. I. Study of the neighborhood of a singular point of a multidimensional differential equation in the analytical case. Dokl. Akad. Nauk SSSR, 1966, Vol. 166, No. 3, pp. 544–547. (10 refs.)

Pilyutik, A. G., and Talalaev, P. A. On improving estimates of solutions for a system of linear differential equations with variable coefficients. PMM, 1965, Vol. 29, Iss. 6.

Pittel, B. G. On an optimal control problem related to the minimization of a "maximum deviation" type functional. Differ. Uravn., 1965, Vol. 1, No. 11, pp. 1493–1508. (10 refs.)

Pliss, V. A. Families of periodic solutions of second-order differential equation systems without dissipation. Differ. Uravn., 1965, Vol. 1, No. 11, pp. 1428–1439.

Plotnikova, G. V. On the stability of periodic solutions of non-autonomous quasi-linear systems with two degrees of freedom. PMM, 1965, Vol. 29, Iss. 6. (5 refs.)

Prilepko, A. I. On the uniqueness of the solution to the external inverse problem of the Newtonian potential. Differ. Uravn., 1966, Vol. 2, No. 1, pp. 107–124. (29 refs.)

Protasov, V. I. The Cauchy problem for a linear differential equation of infinite order. Dokl. Akad. Nauk SSSR, 1965, Vol. 164, No. 4, pp. 743–745.

Pukhnachev, V. V. On an equation with two small parameters at the derivatives. Zh. Vychisl. Mat. Mat. Fiz., 1966, Vol. 6, No. 1, pp. 178–183.

Rakhmatova, Kh. R. On a type of infinite-order differential equation with polynomial coefficients of increasing degrees. Izv. Akad. Nauk UzSSR Ser. Fiz.-Mat. Nauk, 1965, No. 6, pp. 20–29. (6 refs.)

Ryzhov, Yu. M. On calculating the likelihood ratio for Gaussian random processes satisfying certain linear differential equations. Ukr. Mat. Zh., 1966, Vol. 18, No. 1, pp. 124–129. (7 refs.)

Salmanov, Yu. D. The Sturm–Liouville problem for a general linear differential equation. Differ. Uravn., 1965, Vol. 1, No. 10. (11 refs.)

Sapagovas, M. P. On an iterative method for solving a nonlinear ordinary differential equation. Vychisl. Mat., 1965, Iss. 1, pp. 124–133. (6 refs.)

Sobolev, L. G. On the numerical solution of stable linear equations. Tr. TsNII Flota, 1965, Iss. 63, pp. 46–56.

Sobolevsky, P. E. Generalized solutions of first-order differential equations in Banach space. Dokl. Akad. Nauk SSSR, 1965, Vol. 165, No. 3, pp. 486–489. (6 refs.)

Stonitsky, A. A. On the application of A. M. Lyapunov's method to solving the problem of periodic waves of finite amplitude. Vychisl. Mat., 1965, pp. 68–78. (8 refs.)

Surovikhin, K. P. Cartan's exterior forms and finding the fundamental group admitted by a given system of equations. Vestn. Mosk. Univ. Mat. Mekh., 1965, No. 6, pp. 70–75.

Tabueva, V. A. Qualitative investigation of a second-order differential equation in control theory. Differ. Uravn., 1965, Vol. 1, No. 12, pp. 1557–1567. (13 refs.)

Todorov, P. G. Toward the theory of the Riccati equation. Ukr. Mat. Zh., 1966, Vol. 18, No. 1.

Turin, V. Ya. Instability of solutions of a system of differential equations with discontinuous right-hand sides in the critical case. Differ. Uravn., 1965, Vol. 1, No. 10, pp. 1312–1320. (7 refs.)

Faizibaev, E. On the uniqueness of the solution to a second-order nonlinear differential equation. Izv. Akad. Nauk UzSSR Ser. Fiz.-Mat. Nauk, 1965, No. 6, pp. 82–83.

Fedoryuk, M. V. Asymptotics of solutions of ordinary linear differential equations of $n$-th order. Dokl. Akad. Nauk SSSR, 1965, Vol. 165, No. 4, pp. 777–779. (5 refs.)

Fedoryuk, M. V. One-dimensional scattering problem in the semiclassical approximation. Differ. Uravn., 1965, Vol. 1, No. 11, pp. 1525–1536. (13 refs.)

Fomin, V. N. Parametric resonance of elastic systems with an infinite number of degrees of freedom. II. Vestn. Leningr. Univ. Mat. Mekh. Astron., 1965, No. 19, Iss. 4, pp. 74–86. (5 refs.)

Khaimov, N. B. On the distribution of singular points for a differential equation. Dokl. Akad. Nauk TadzhSSR, 1965, Vol. 8, No. 6, pp. 3–6.

Khodzhanov, A. S. Stability of controlled systems with tachometric feedback. Vestn. Akad. Nauk KazSSR, 1965, No. 10, pp. 74–76. (5 refs.)

Tsarkov, E. F. Nonlinear self-oscillations in a system described by a second-order stochastic differential equation with constant delay. Izv. Akad. Nauk LatvSSR Ser. Fiz. Tekh. Nauk, 1965, No. 4, pp. 53–59. (6 refs.)

Tsoi, P. V. On a problem for a system of differential equations of energy and mass transfer. Differ. Uravn., 1965, Vol. 1, No. 10. (8 refs.)

Chekmarev, T. V. On the solution of the Tricomi problem for systems of differential equations. Izv. Vyssh. Uchebn. Zaved. Mat., 1966, No. 1, pp. 147–152.

Cheresiz, V. M. On almost-periodic solutions of nonlinear systems. Dokl. Akad. Nauk SSSR, 1965, Vol. 165, No. 2, pp. 281–284. (5 refs.)

Chernyatin, V. A. On the solvability of the problem of analytical regulator construction for non-autonomous systems. Avtom. Telemekh., 1965, Vol. 26, No. 11, pp. 1889–1899. (10 refs.)

Shafiev, R. A., and Kerimova, D. N. On the approximate solution of a nonlinear problem in filtration theory. Dokl. Akad. Nauk AzerbSSR, 1965, Vol. 21, No. 5, pp. 8–12.

Shilyak, D. D. Application of the Mikhailov criterion for investigating the degree of stability and oscillation of linear pulse systems. Avtom. Telemekh., 1965, Vol. 26, No. 7, pp. 1297–1301.

Shilman, S. V. On the absolute stability of nonlinear controlled systems with periodically varying parameters. Izv. Vyssh. Uchebn. Zaved. Radiofiz., 1965, Vol. 8, No. 5, pp. 1016–1029. (11 refs.)

Shkil, N. I. Construction of a general asymptotic solution for a system of linear differential equations with a small parameter. Izv. Vyssh. Uchebn. Zaved. Mat., 1966, No. 1, pp. 161–169.

Yakovlev, M. K. On a method for constructing Lyapunov functions for linear systems with variable coefficients. Differ. Uravn., 1965, Vol. 1, No. 11.

Yaroshevich, G. O. Linearization of the equations of motion of autonomous systems using asymptotic polynomials. Izv. Vyssh. Uchebn. Zaved. Mat., 1965.

(To be continued)