Geodesic

Sommaire du Fascicule no. 1

Global solution of the Tricomi problem for a class of nonlinear differential equations of mixed type
p. 3-10
Solvability of certain boundary value problems for elliptic systems with a degeneration of the order on the boundary
p. 11-18
On the question of stability of mixed problems for a quasi-linear equation
p. 19-29
Inverse problems of potential theory
p. 30-44
On a boundary value problem for an equation of mixed type with two lines of parabolic degeneration
p. 45-58
On the Dirichlet problem for certain elliptic systems of second order
p. 59-68
On the theory of singular integral equations
p. 69-80
The Dirichlet problem for degenerating nonlinear elliptic equations
p. 81-88
Unconditional solvability of the oblique derivative problem
p. 89-96
On a particular case of the Dirichlet problem for the Darboux equation for the space slit along an ellipsoidal disc
p. 97-108
On the spectrum of a differential operator connected with a mixed problem
p. 109-113
Fundamental solutions of $B$-elliptic equations
p. 114-129
Imbedding theorems for mixed spaces
p. 130-138
Mixed derivatives of functions summable with a weight
p. 139-154
On the Dirichlet problem for elliptic systems in space
p. 155-157
Jurii Alekseevich Mitropol'skii
p. 158-166
A letter to the editors: Corrections

Sommaire du Fascicule no. 2

Stability of generalized processes.~I, II
p. 171-179
Construction of a set of systems of differential equations having prescribed integrals
p. 180-192
On the structure of the coefficients of the succession function
p. 193-205
On the behavior as $x\rightarrow +\infty $ of solutions of ordinary differential equations and algebraic equations with monotone coefficients
p. 206-218
Analytic form of solutions of linear systems of differential equations with quasi-periodic coefficients
p. 219-225
Asymptotic trajectories of non-autonomous dynamical systems
p. 226-231
Stability of the trivial solution of a non-autonomous system of two differential equations
p. 232-243
Application of generalized Ljapunov functions to the investigation of non-homogeneous systems
p. 244-249
On the spectrum of a non-selfadjoint Sturm--Liouville operator
p. 250-263
On the question of existence of solutions of systems of singular integral equations of Volterra type
p. 264-272
Uniqueness theorems for a system of multidimensional Volterra integral equations
p. 273-277
On a singular integro-differential equation
p. 278-293
Asymptotic representation of the solution of a mixed problem for a differential equation of hyperbolic type with a small parameter
p. 294-314
The first boundary value problem for elliptic equations of second order
p. 315-326
Expansion formulas for a boundary value problem with a complex parameter
p. 327-340
Uniqueness theorems for ordinary differential equations
p. 341-347
Representability of spatial boundary value problems in the form of a system of plane boundary value problems
p. 348-350
Investigation of stability of discontinuous solutions of gas dynamics equations
p. 351-353
Новые книги
p. 354-355

Sommaire du Fascicule no. 3

Topological classification of singular points and generalized Ljapunov functions
p. 359-370
On a class of motions of a pendulum in a medium with large resistance
p. 371-379
The synthesis of optimal controls in nonlinear oscillatory systems of second order
p. 380-394
Differential equations and inequalities with discontinuous right member. I
p. 395-409
Fredholm integral equations of the first kind
p. 410-421
Expansion of an arbitrary function in an integral with respect to the squares of Legendre functions with complex index
p. 422-435
On the problem of controllability of linear systems with aftereffect
p. 436-445
The theory of characteristic vectors and its application to the study of the asymptotic behavior of solutions of differential systems. I
p. 446-467
Systems of differential equations whose critical singular points are fixed
p. 468-478
Controllability in a Hilbert space
p. 479-484
An elliptic system of partial differential equations with a singular point at the origin
p. 485-495
Solutions of long wave type for quasilinear elliptic equations in an unbounded strip
p. 496-508
Complex eigenvalues of a non-selfadjoint operator
p. 509-513
An example of a composite stationary point
p. 514-519
On a class of solutions of the sixth Painlev\'e equation
p. 520-523
Bounded solutions of differential equations of second order
p. 524-528

Sommaire du Fascicule no. 4

Ljapunov's first method
p. 531-578
Asymptotic behavior of solutions of nonlinear controlled systems
p. 579-588
On the definition of the capture regions in the case of a system of linear differential equations with periodic coefficients
p. 589-600
Representations of a solution of a system of linear differential equations in a neighborhood of an irregular singular point
p. 601-618
Investigation of nonlinear vibrations of thin plates with consideration of damping
p. 619-635
Incorrect problems with a closed non-invertible operator
p. 636-646
A linear parabolic problem in a cylinder, infinite with respect to time. Stabilization of solutions
p. 647-666
Application of a theorem of Hart to the investigation of nonlinear integral equations
p. 667-679
The first boundary value problem for quasilinear parabolic systems with retarded argument
p. 680-686
Refinement of a theorem of V. V. Morozov
p. 687-691
A remark on limit cycles of an equation
p. 692-694
Solvability of an integro-differential equation
p. 695-697
A remark on the method of fictitious regions
p. 698-701
А.\,В.~Бицадзе. Краевые задачи для эллиптических уравнений второго порядка
p. 702-703

Sommaire du Fascicule no. 5

The basic existence theorems of space elasticity theory
p. 707-721
Recurrent motions of periodic systems of two differential equations
p. 722-732
A method of stabilization of control systems
p. 733-741
A nonlinear analog of the Ljapunov transformation
p. 742-748
Movable singularities of systems of differential equations
p. 749-760
Solutions of a system of integro-differential equations in the neighborhood of a singular point
p. 761-770
The theory of Painlev\'e's fourth equation
p. 771-780
Perturbations of a differential equation
p. 781-786
Weakly irregular system
p. 787-795
Asymptotic stability of the zero solution of a non-autonomous system of two differential equations. I
p. 796-810
A problem of N. P. Erugin on integrability by quadratures of a system of ordinary differential equations
p. 811-819
Calculational formulas and asymptotics, with estimates of the function $F(x)=\sum_{k=0}^\infty\frac{z^k}{(k!)^2}$
p. 820-830
Generalized Emden--Fowler equation
p. 831-838
Differential equations and inequalities with discontinuous right hand sides. II
p. 839-848
Families of extremals
p. 849-851
The construction of a family of integral lines situated in a prescribed region
p. 852-856
Integration in finite form of certain systems of ordinary second order differential equations
p. 857-861
Asymptotic behavior of integrals of quasiperiodic functions
p. 862-868
Николай Павлович Еругин (к~60-летию со дня рождения)
p. 869-872

Sommaire du Fascicule no. 6

Asymptotic series in the theory of nonlinear systems of ordinary differential equations. I
p. 875-889
A priori estimate of solutions of boundary value problems for second order ordinary nonlinear differential equations
p. 890-897
Differential equations $yy'=Q_4(x,y)$, having an ellipse as limit cycle
p. 898-904
On the question of non-uniqueness of solutions of systems of singular integral equations of Volterra type
p. 905-911
The group of symmetric transformations of a generalized Gyld\'en problem
p. 912-918
The existence of bounded and periodic solutions of integro-differential equations with retarded argument
p. 919-925
The asymptotic behavior of solutions of certain nonlinear differential equations
p. 926-940
A formula for the expansion of an arbitrary matrix-function in terms of the solution of a spectral problem
p. 941-947
Smoothness of thermal potentials. IV. Application of the theory of thermal potentials to the solution of a problem of biophysics on the distribution of concentrations in a living cell
p. 948-964
A problem on a pairing of equations of parabolic and hyperbolic types when time derivatives occur in the boundary conditions
p. 965-979
The second boundary value problem for the differential equation of elastic equilibrium of a slanting cylindrical shell
p. 980-993
Solution of a completely hyperbolic equation with initial data given on a line of degeneracy
p. 994-1001
Solution by the method of lines of certain boundary value problems for equations of elliptic type
p. 1002-1008
Conditions of validity of {\v C}aplygin's theorem for elliptic difference equations
p. 1009-1021
Integrability conditions of certain second order nonlinear differential equations
p. 1022-1024
Linear boundary value problems with small lag
p. 1025-1028
The structure of a solution of the equation $u'=U_0(\nu)u+\sum_{n=1}^\infty(\nu)u^{1+\alpha_n}\equiv U(u,\nu)$ in a small
p. 1029-1030
Vladimir Ivanovic Smirnov (zum 80. Geburtstag)
p. 1031-1034

Sommaire du Fascicule no. 7

A priori estimates for the derivatives of bounded functions satisfying second-order differential inequalities
p. 1043-1052
A class of dynamical systems with stable structures
p. 1053-1059
Stability of a singular cycle in the critical case
p. 1060-1069
Asymptotic series in the theory of nonlinear systems of ordinary differential equations. II
p. 1070-1077
Secant sets of dynamical systems
p. 1078-1083
A question on the uniqueness of solutions of linear boundary value problems for ordinary differential equations
p. 1084-1087
Sufficient conditions for the existence of bounded solutions of a system of differential equations
p. 1088-1094
A question on rough systems with aftereffect
p. 1095-1099
Quasiperiodic solutions of nonlinear systems of differential equations containing a small parameter
p. 1100-1112
Control of motion of a quasilinear system
p. 1113-1118
Solutions of Volterra's multi-dimensional integral equation in the neighborhood of a singular point
p. 1119-1126
Cauchy's formula and conditions of stability for the solutions of an integro-differential equation
p. 1127-1134
Incorrect problems in Hilbert space and stable methods of solving them
p. 1135-1156
A nonlinear differential equation with a polynomial functional generating it
p. 1157-1165
On the Dirichlet problem for equations with a degeneracy at infinity
p. 1166-1179
Рассеяние наклонно падающей плоской электромагнитной волны на двух соосных круговых дисках
p. 1180-1194
The theory of Macdonald integrals. I. Recurrent relations. Uniformly convergent series
p. 1195-1212
Properties of integrals along a parabola, and Born's scattering theory approximations
p. 1213-1220

Sommaire du Fascicule no. 8

Periodic generalized orbits
p. 1231-1239
Zur Frage der Stabilit\"at einer Klasse von Relaissystemen
p. 1240-1247
Sufficient conditions for the absence of periodic trajectories of autonomous systems in the case of multiply connected regions
p. 1248-1252
Some problems on the quieting of a linear system
p. 1253-1258
The highest exponent and the critical exponent of certain differential equations in a Banach space
p. 1259-1265
Application of the asymptotic method to the integration of autonomous systems with lag
p. 1266-1272
A particular solution of an integro-differential equation with deviating argument of neutral type
p. 1273-1281
Classification of the singular points of linear systems of total differential equations
p. 1282-1291
L\"osung von Aufgaben der Theorie des W\"arme- und Massentransports
p. 1292-1298
An existence and uniqueness theorem for the Cauchy problem of a hyperbolic equation with self-regulating delay
p. 1299-1302
On the smoothness of thermal potentials. IV
p. 1303-1312
Estimates of the domain of solvability for the system of equations of a moment-free reticulated cylindrical shell in the case of the first boundary value problem
p. 1313-1324
More on exact estimates in Rothe's method
p. 1325-1333
The first boundary value problem for quasilinear parabolic equations with retarded argument
p. 1334-1341
Integral equations for periodic solutions of the generalized Lam\'e equation
p. 1342-1354
Boundary value problems for the equation $\Delta^mu=0$
p. 1355-1363
The asymptotic distribution of the eigenvalues of elliptic operators in $n$-dimensional space
p. 1364-1374
Estimates in a closed region of the eigenfunctions of an elliptic operator with discontinuous coefficients
p. 1375-1392
On the existence of an upper and a lower solution of a boundary value problem for a system of ordinary differential equations
p. 1393-1396
The eigenfunction expansion of a singular boundary value problem for Legendre's equation
p. 1397-1399
The resolvent of a weighted integro-differential equation
p. 1400-1402
Viktor Vladimirovi{\v{c}} Nemycki{\v\i}
p. 1403-1404

Sommaire du Fascicule no. 9

A qualitative investigation of a certain differential equation of the second order in control theory. II
p. 1415-1426
The stability of a certain third-order system with variable structure
p. 1427-1436
Bounded and oscillatory solutions of the system $\ddot x+g(x,\,\dot x)=\bar 0$
p. 1437-1449
Recurrent solutions of differential equations and the general theory of dynamical systems
p. 1450-1460
Regularity of a class of linear systems with almost periodic coefficients
p. 1461-1470
On a theorem of Carath\'eodory
p. 1471-1476
An investigation of a system of equations describing the motion of a spherical pendulum in the case of the presence of a resistance
p. 1477-1483
The Sturm--Liouville problem of a second order nonlinear ordinary differential equation
p. 1484-1494
The topological equivalence of systems of total differential equations in neighborhoods of closed trajectories
p. 1495-1507
Comparison of the accuracy of numerical integration of second-order differential equations and the corresponding system of first-order differential equations
p. 1508-1517
Das Problem der Querschwingungen eines viskoelastischen Stabes
p. 1518-1536
The asymptotic representation of the solution of a boundary value problem for a system of ordinary differential equations with a complex parameter
p. 1537-1542
Das Feld eines horizontalen magnetischen Dipols in Gegenwart eines Ellipsoids
p. 1543-1551
Grenzwert der L\"osung der Wellengleichung f\"ur ein inhomogenes Medium f\"ur $t\to\infty$
p. 1552-1559
The solution of singular Cauchy problems in basis series
p. 1560-1577
Investigation of a mixed problem for a class of third-order quasilinear differential equations
p. 1578-1591
Branching of solutions of the Cauchy problem for a class of nonlinear integro-differential equations
p. 1592-1601
The solution of a boundary value problem by the method of $R$-functions
p. 1602-1605
The convergence of the method of collocation by lines
p. 1606-1613
Новые книги
p. 1614-1615

Sommaire du Fascicule no. 10

Conditions for the existence of recurrent trajectories in dynamic systems with a cylindrical phase space
p. 1627-1633
Dissipativity and periodic solutions of second order nonsymmetric systems
p. 1634-1642
A periodic boundary value problem for the differential equation $y^{(n)}+f(t,y,y',\dots,y^{(n-1)})=0$
p. 1643-1655
The theory of characteristic vectors and its application to the study of the asymptotic behavior of solutions of differential systems.~II
p. 1656-1672
On inverse problems of the qualitative theory of differential equations
p. 1673-1681
The number of periodic solutions of the second kind to the differential equation $\ddot{\varphi}-f_1(\varphi)\dot{\varphi}-f_0(\varphi)=0$
p. 1682-1691
Nonlinear differential equations in a Banach space, close to linear ones
p. 1692-1706
A sufficient test for the stability of the trivial solution of a third-order differential equation with periodic coefficients
p. 1707-1717
A method for the approximate realization of a motion along a given trajectory
p. 1718-1724
On averaging in systems of integro-differential equations
p. 1725-1731
The asymptotic behavior of solutions of a class of Volterra's integro-differential equations
p. 1732-1744
Some properties of functions which satisfy elliptic equations of higher order
p. 1745-1750
The theory of Macdonald integrals. II. Asymptotic expansions
p. 1751-1765
The completeness of certain function systems
p. 1766-1771
A method for introducing the finite parts of divergent integrals, and applications of them in operational calculus
p. 1772-1781
The application of Galerkin's method to the solution of a mixed problem for a quasilinear hyperbolic equation
p. 1782-1791
On the problem of the analytic construction of regulators
p. 1792-1795
A partial differential equation with retarded argument
p. 1796-1800
Иосиф Захарович Штокало (к~70-летию со дня рождения)
p. 1801-1809

Sommaire du Fascicule no. 11

50 лет новой эры
p. 1819-1820
The analytic theory and problems in the real theory of differential equations, connected with the first method and with methods of the analytic theory
p. 1821-1863
The existence of invariant tori in the neighborhood of the zero solution of a system of ordinary differential equations
p. 1864-1881
An approach to nonlinear boundary value problems for ordinary differential equations
p. 1882-1888
\"Uber die Vereinfachung der Differentialgleichungen der Pr\"azession eines Kreisels mit zwei Freiheitsgraden bei der Untersuchung der Rotationsbewegung eines K\"orpers
p. 1889-1894
A question on the asymptotic solution of an optimal control problem
p. 1895-1902
Periodic solutions of second-order nonlinear equations
p. 1903-1912
On the theory of Painlev\'e's third equation
p. 1913-1923
The function space $W_p^m,\alpha_1,\dots,\alpha_s(T,\Omega)$, and completely continuous operators in weight spaces
p. 1924-1941
Asymptotic methods in the theory of one-dimensional singular differential operators of odd order
p. 1942-1956
On the theory of operators of the form $\frac{d^m}{dt^m}-A$
p. 1957-1970
Представление электромагнитных полей, порожденных диполями в~присутствии
p. 1971-1989
Two-point and multi-point Taylor formulas
p. 1990-1998
Kontaktaufgabe f\"ur eine lineare deformierbare Grundlage
p. 1999-2002
Some remarks concerning a differential equation of arbitrary order
p. 2003-2006

Sommaire du Fascicule no. 12

The classification of trajectories of a dynamical system with cylindrical phase space
p. 2015-2020
The concept of stability with respect to a generalized perturbation
p. 2021-2029
Oscillations of a pendulum with relay control
p. 2030-2036
Analysis of a certain class of systems of differential-difference equations by the method of separation of motions
p. 2037-2046
Conditions for the existence of circular motions of Froude's connected pendulums
p. 2047-2052
Some theorems on limit cycles
p. 2053-2057
\"Uber ein Verfahren zur Organisation des Gleitens in einem dynamischen System
p. 2058-2066
The existence of optimal controls in systems with lag
p. 2067-2080
The minimization of a convex functional by the free trajectories of a linear system
p. 2081-2093
On the approximation of linear differential equations with lag
p. 2094-2107
Regularization of certain pursuit problem
p. 2108-2121
The existence of a domain of accessibility
p. 2122-2126
The connection between the stability of characteristic exponents and almost reducibility of systems with almost periodic coefficients
p. 2127-2134
Systems of differential equations with algebraic moving singular points
p. 2135-2143
The choice of the right-hand sides in the system of differential equations of the gradient method
p. 2144-2150
Conditions for the existence of bounded solutions of a difference equation in a Banach space
p. 2151-2160
The asymptotic equivalence of the solutions of certain linear systems of differential equations
p. 2161-2176
Dynamical systems close to Hamiltonian ones
p. 2177-2178
Евгений Алексеевич Барбашин (к~50-летию со дня рождения)
p. 2179-2183
Рецензия на книгу Е.\,А.~Барбашина «Введение в~теорию устойчивости»
p. 2184-2185
Поправка к~статье: «Поле горизонтального магнитного диполя в~присутствии сфероида» (т.~3, \No~9, 1967)