Geodesic

Sommaire du Fascicule no. 1

A boundary value problem for a certain degenerate hyperbolic equation, and singular integral equations of the third kind
p. 3-14
The first boundary value problem for certain strongly elliptic systems of equations that degenerate on the boundary
p. 15-24
Some boundary value problems for a certain degenerate hyperbolic equation of the second kind
p. 25-33
The uniqueness of the solution of the exterior contact inverse problem of the theory of the logarithmic potential
p. 34-39
The asymptotic behavior of the solutions of a certain mixed problem
p. 40-48
The Darboux problem for degenerate hyperbolic equations
p. 49-56
The problem of A. V. Bicadze for an equation of mixed type in multidimensional domains
p. 57-63
Exterior Dirichlet and Neumann problems for the polyharmonic equation
p. 64-72
A certain quasilinear parabolic equation
p. 73-80
A certain method of expanding a solid metaharmonic potential in an integro-power series
p. 81-93
Mixed inverse problems of potential theory in the case of contact bodies
p. 94-108
The asymptotic behavior as $t\rightarrow \infty $ of a positive solution of a boundary value problem for a model equation of chemical kinetics
p. 109-114
The behavior of the solutions of mixed problems for quasilinear equations of parabolic type
p. 115-120
The Dirichlet problem for the elliptic system of A.\,V.~Bicadze with lower derivatives
p. 121-134
The spectrum of a certain operator
p. 135-141
A representation of the analytic solutions of certain partial differential equations whose coefficients have pole type singularities with respect to only one argument
p. 142-156
A generalized Fourier transform and asymptotic behavior of the solutions of the telegrapher's equation
p. 157-165
On the Dirichlet problem for degenerate elliptic equations
p. 166-174
A certain boundary value problem with nonlinear boundary conditions that have a discontinuity
p. 175-177
A criterion for the uniqueness of the solution of the Darboux problem for a certain degenerate hyperbolic equation
p. 178-181
The uniqueness of the strong solution of the generalized Tricomi problem
p. 182-186

Sommaire du Fascicule no. 2

Николай Иванович Мусхелишвили (к~80-летию со дня рождения)
Asymptotic representation of the solutions of a certain system of two differential equations
p. 196-204
The oscillatoriness of the solutions of second order differential equations
p. 205-214
Certain functional methods in the theory of almost periodic solutions.~I
p. 215-225
Certain sufficient tests for the existence of limit cycles of a certain dynamic system
p. 226-231
Exponential solutions of the Cauchy problem with a constant operator
p. 232-243
The eigenfunction expansion of a second order differential equation with one turning point
p. 244-260
The structural stability of a sequence of linear systems of second order differential equations with periodic coefficients
p. 261-270
Estimates of the solutions of certain systems of differential equations with time lag
p. 271-278
The qualitative behavior of the trajectories of a certain class of differential systems
p. 279-285
The eigenfunction expansion for the Schr\"odinger operator
p. 286-296
The stabilization of the solution of the Cauchy problem for a parabolic equation
p. 297-311
On the Gevrey theory for parabolic potentials.~I, II
p. 312-328
The stabilization of the solution of a boundary value problem for a fourth order parabolic equation
p. 329-343
Optimal approximate methods for the solution of linear problems
p. 344-352
Transformations of ordinary nonlinear differential equations
p. 353-356
The approximate solution of singular integro-differential equations by the method of averaging of functional corrections
p. 357-358
The isochrony of a certain system of differential equations
p. 359-362
The perturbations that preserve the stability property
p. 363-364
Sets of bilateral attraction
p. 365-367
The computation of the quadratic functional in a certain special case
The computation of quadratic functionals for systems with time lag
p. 369-370
Necessary and sufficient conditions for the realizability of the limiting amplitude principle
p. 371-372
The eigenfunction expansion of a certain linear operator
p. 373-375
Linear zero-divergence transformations and the Hall effect
p. 376-377
Letter to the editor
Letter to the editor

Sommaire du Fascicule no. 3

Linear systems of ordinary differential equations
p. 387-390
The optimal processes in linear systems that do not satisfy the nondegeneracy condition
p. 391-396
The boundedness of the solutions of a certain class of differential-difference equations with lags of the argument
p. 397-408
An investigation of a system of three differential equations with a functional parameter
p. 409-418
The structural stability of certain systems of differential equations
p. 419-423
A model example of the pursuit game problem with incomplete information. I
p. 424-435
The problem of evasion in linear differential games
p. 436-445
The periodic solutions of autonomous systems of neutral type equations with small lag
p. 446-452
Synthesis and analysis of a certain fourth order control system by the phase plane method
p. 453-460
A classification of integral varieties of a homogeneous three-dimensional system by the structure of the limit sets
p. 461-470
A certain problem of the conjugacy of a hyperbolic and a parabolic system of equations
p. 471-485
Representation of functions of two variables by means of differentiable trigonometric series for the solution of partial differential equations
p. 486-500
Three approaches to the solution of the generalized Dirichlet and Neumann problems for second order elliptic equations
p. 501-509
Stable summability methods for Fourier series
p. 510-518
Bounded, periodic and almost periodic solutions of elliptic equations
p. 519-529
A certain iteration process for the solution of a boundary value problem
p. 530-533
The localization of eigenfunction expansions of a selfadjoint elliptic operator
p. 534-537
On the question of the relay stabilization of programmed motions
p. 538-539
The limit cycles of pendulum systems with impulse perturbation
p. 540-542
The stability of a system of differential equations of lagging type
p. 543-544
The M. V. Keldy{\v s} series
p. 545-548
Calder\'on--Zygmund singular integral operators on classes of functions with a given order of decrease at infinity
p. 549-552
Ivan Georgevi{\v{c}} Petrovski{\v\i} (On his seventieth birthday)
p. 553-564
Первый фундаментальный труд по истории отечественной математики
p. 565-566

Sommaire du Fascicule no. 4

Generalized regular systems
p. 575-591
Conditions for the applicability of {\v C}aplygin's theorem to a certain multipoint linear difference boundary value problem of order $n$
p. 592-602
Asymptotic series for the eigenvalues and eigenfunctions of second order self-adjoint operators
p. 603-614
The asymptotic stability of sets in dispersive dynamical systems
p. 615-621
A second order dynamical system with a given particular integral
p. 622-630
Ideally observable systems
p. 631-638
Periodic solutions of systems of linear equations of general form with deviating argument
p. 639-650
The behavior of the solutions of a sequence of second order periodic systems with a small nonlinearity
p. 651-660
The third exterior boundary value problem for a second order elliptic equation. I
p. 661-669
Conditions for the convergence of spectral decompositions that correspond to self-adjoint extensions of elliptic operators. I. Self-adjoint extension of the Laplace operator with a point spectrum
p. 670-710
On the Gevrey theory for parabolic potentials. I, II
p. 711-726
Closure in the metric of the generalized Dirichlet integral
p. 727-736
Expansion in eigenfunctions of a nonselfadjoint differential operator of an exterior boundary value problem
p. 737-742
The order of the convergence of the method of least squares for the Dirichlet problem
p. 743-746
The behavior of the solution of systems of two differential equations in the neighborhood of an essential singularity
p. 747-749
The problem of the conjugacy of certain nonstationary differential equations of order $2m$
p. 750-753
Coefficient stability of the solutions of second order ordinary differential equations and of parabolic equations on the plane
p. 754-758
A certain one-dimensional scattering problem in the quasi-classical approximation
p. 759-762

Sommaire du Fascicule no. 5

A representation of the solutions of a certain system of differential equations with periodic coefficients
p. 771-781
The separatrices and limit cycles of certain differential equations
p. 782-790
On the question of the general form of a linear equation.~I, II
p. 791-797
The influence of strong dynamical perturbations on the behavior of the solutions of autonomous linear differential systems
p. 798-806
Non-zero solutions of boundary value problems
p. 807-813
A qualitative investigation of first order differential-operator equations of stable type with lag
p. 814-826
Existence of a value of a pursuit game
p. 827-839
A certain version of the closing lemma
p. 840-850
Conditions for the convergence of spectral decompositions that correspond to self-adjoint extensions of elliptic operators. II. Self-adjoint extension of the Laplace operator with an arbitrary spectrum
p. 851-882
A certain class of second order nonlinear differential equations
p. 883-891
A diffraction problem for the radiation field of a biased magnetic dipole on two coaxial circular disks. I, II
p. 892-901
Regular linear difference systems
p. 902-909
A fundamental theorem on critical cases of difference systems
p. 910-918
A certain integro-differential equation with a small parameter multiplying the derivative in the case when the degenerate equation occurs in the spectrum
p. 919-922
Some stability criteria for the solutions of equations that are not solved with respect to the highest derivative
p. 923-926
The oscillatoriness of the solutions of a nonlinear equation of higher order
p. 927-929
The zeros of the oscillatory solutions of the equation $x''+a(t)f(x)=0$
p. 930-933
Asymptotic estimates of the Green's function of singularly perturbed differential operators with almost periodic coefficients
p. 934-936
A criterion for uniform asymptotic stability with respect to a non-autonomous homogeneous approximation of order $m\geq 1$
p. 937-940
Konstantin Petrovi{\v{c}} Persidski{\v\i}
p. 941-945

Sommaire du Fascicule no. 6

An investigation of the stability of the solutions of a system of second order linear differential equations with periodic coefficients
p. 955-960
The oscillatoriness and non-oscillatoriness of the solutions of vector differential equations
p. 961-969
An asymptotic expansion of the solutions of the equation $y^{\mathrm{IV}}+(\lambda+\xi^2)y^{\mathrm{II}}\mu y=0$
p. 970-980
On the question of the general form of a linear equation. I, II
p. 981-989
A refinement of the estimate in the freezing method for a two-dimensional system with coincident characteristic numbers
p. 990-996
Oscillations in certain essentially nonlinear systems
p. 997-1006
The periodic solutions of second and third order linear systems
p. 1007-1011
Stabilization of nonstationary linear systems with discrete control
p. 1012-1016
The Goursat problem for abstract second order linear differential equations
p. 1017-1030
A diffraction problem for the radiation field of a biased magnetic dipole on two coaxial circular disks.~I, II
p. 1031-1035
Conditions for the convergence of spectral decompositions that correspond to self-adjoint extensions of elliptic operators. III.~Best possible local estimates of Riesz means of an arbitrary function from the class $L_2(G)$ for a self-adjoint extension of the Laplace operator
p. 1036-1041
Radial transformation operators
p. 1042-1056
Certain boundary value problems for elliptic singular integrodifferential equations in two-dimensional domains
p. 1057-1064
An application of the method of the contour integral to the solution of a mixed problem for a parabolic system with variable coefficients
p. 1065-1076
A theory of the functional equations of Malju{\v z}inec. III. In homogeneous functional equations. General theory
p. 1077-1088
The first boundary value problem for a certain ultraparabolic equation
p. 1089-1096
Asymptotic estimates of the solutions of a certain class of nonlinear integro-differential equations
p. 1097-1107
Generalized solution of an equation with discontinuous operator
p. 1108-1113
The reducibility of certain linear differential systems
p. 1114-1115
Solutions of constant sign for equations of neutral type
p. 1116-1119
The continuous dependence of the solution of an optimal control problem with free time on the initial data
p. 1120-1123
On the theory of Painlev\'e's second equation
p. 1124-1125
An investigation of the integral curves of a homogeneous equation in the large on the whole plane
p. 1126-1127
Uniqueness and continuous dependence on initial conditions of the solutions of certain systems with transformed argument
p. 1128-1129
Integral equations with deviating argument
p. 1130-1132
The asymptotic behavior of the solution of a quasilinear system of Volterra integral equations with constant retardation of the argument
p. 1133-1134
Solutions of Painlev\'e's second equation that are extendable to the whole real axis
p. 1135-1136

Sommaire du Fascicule no. 7

The zeros of the solutions of a second order linear differential equation with retarded argument
p. 1147-1157
A function of the boundary value conditions and estimation of the Green's function of a periodic problem
p. 1158-1170
The coming together of quasilinear objects in the regular case
p. 1171-1178
Cases of sharpening and the attainability of an estimate of the highest exponent in the method of freezing
p. 1179-1191
On the theory of complete controllability of linear systems of differential equations with retarded argument
p. 1192-1198
The position of the separatrices of saddle-point periodic motions of systems of second order differential equations
p. 1199-1225
A certain boundary value problem for an elliptic system of special form
p. 1226-1234
Transformation formulae of radial type
p. 1235-1249
``Resonance'' representations of the solutions of a first order hyperbolic system in the plane
p. 1250-1262
The solution of one-dimensional problems for a second order parabolic system in unbounded domains
p. 1263-1275
A theory of functional equations of Malju{\v z}inec. IV. Nonhomogeneous functional equations with periodic coefficients
p. 1276-1287
Differential properties of the extremals of quadratic functionals with discontinuous coefficients
p. 1288-1293
Eigenfunctions of the Hammerstein operator
p. 1294-1304
An approximate solution of the Cauchy problem for linear Fredholm integro-differential equations by the method of averaging of functional corrections
p. 1305-1314
A certain method of constructing an approximate solution of first order differential equations
p. 1315-1319
The control of rotational motion
p. 1320-1322
The potentials for a certain type of higher order elliptic equations
p. 1323-1326
The convergence property of certain third order nonlinear differential equations
p. 1327-1329
Behavior of the solution on the half-axis of a certain second order nonlinear differential equation
p. 1330-1332
The absolute and uniform convergence of the generalized Fourier integral
p. 1333-1338

Sommaire du Fascicule no. 8

The existence of conditionally periodic solutions of systems of differential equations
p. 1347-1356
Expansion of the solutions of a certain autonomous system in a certain singular stability case
p. 1357-1367
On the question of the sign of the Green's function of a difference problem with combined boundary value conditions
p. 1368-1376
Existence theorems and uniqueness classes of the solutions of functional equations with heredity
p. 1377-1384
Differentiability of a mapping that describes isochrone surfaces in a linear time optimal problem
p. 1385-1392
Local behavior of the solutions of ordinary differential equations
p. 1393-1397
Differential approach games in systems with lag
p. 1398-1409
The existence of a local invariant surface in the absence of linear approximation
p. 1410-1418
The almost-periodicity of the solutions of a certain class of systems of stochastic differential equations
p. 1419-1428
A certain boundary value for a fourth order equation of mixed type
p. 1429-1439
A boundary value problem for a first order elliptic equation on the plane
p. 1440-1448
An isomorphism of generalized H\"older classes
p. 1449-1458
Estimates near the boundary of generalized solutions of certain classes of second order quasilinear elliptic equations
p. 1459-1472
On the Gevrey theory for parabolic potentials. III
p. 1473-1489
A mean value formula for the eigenfunctions of a second order elliptic selfadjoint operator
p. 1490-1502
The equations of parabolic type with nonpower nonlinearities
p. 1503-1511
Integral estimates in the $L_p$ metric of the derivatives of a polyharmonic function in an $n$-dimensional domain, and certain applications of them
p. 1512-1519
A note on the Bloch theorem
p. 1520-1521
The integral curves of a certain dynamical system
p. 1522-1524
On the question of separatrices and limit cycles of a certain differential equation
p. 1525-1527
The behavior of the solutions of a certain first order differential equation
p. 1528-1530
The norm of an element as a regularizing functional
p. 1531-1533
A certain initial problem for differential equations with retarded argument
p. 1534-1537

Sommaire du Fascicule no. 9

Certain solutions of systems of ordinary differential equations with polynomial right hand side. I, II
p. 1547-1559
Investigation of a singular point on the plane in the case of two zero roots
p. 1560-1567
Absolute stability of direct control systems in two critical cases
p. 1568-1574
A generalized Cauchy problem for a system of differential equations not solved with respect to the derivatives
p. 1575-1580
A maximum principle for general discrete systems
p. 1581-1590
On the optimization of control systems in the presence of constraints. I, II
p. 1591-1602
The branching of solutions of a certain boundary value problem for a second order ordinary differential equation
p. 1603-1610
A certain boundary value problem for a system of ordinary differential equations
p. 1611-1616
Fourier--Bessel series for functions that are integrable with respect to a weight
p. 1617-1628
A conjugation problem for non-stationary abstract linear differential equations
p. 1629-1638
On the question of the solvability of linear differential equations in spaces of analytic functions
p. 1639-1648
The method of lines for nonlinear elliptic equations of arbitrary order
p. 1649-1654
The Neumann problem for piece-wise smooth domains
p. 1655-1666
The stability of the system of eigenvalues and eigenfunctions of the Sturm--Liouville problem
p. 1667-1671
Limit theorems on the existence of integral surfaces that are tangent to singular integral elements
p. 1672-1683
The behavior of solutions of second order parabolic equations with dissipation
p. 1684-1695
Properties of the solutions of a problem with losses in the case of periodic intensities
p. 1696-1698
Conditions for the synthesis of linear controls
p. 1699-1700
Detection of stability of periodic flows with the aid of generalized characteristic numbers
p. 1701-1703
The stability in the critical case of pure imaginary roots, with internal resonance
p. 1704-1706
Stability of quasi-solutions for equations with a closed operator
p. 1707-1709
A certain new method of solution for the biharmonic equation
p. 1710-1713
Periodic boundary value problems and Riesz bases
p. 1714-1720
Algebraic solutions of Abel's differential equation
p. 1721-1722
The simultaneity of systems of two differential equations
p. 1723-1726

Sommaire du Fascicule no. 10

Certain solutions of systems of ordinary differential equations with polynomial right hand side.~I, II
p. 1739-1751
The stability in the large of the zero solution of certain fifth order nonlinear differential equations
p. 1752-1764
The structure of solutions of a certain system of two differential equations. I
p. 1765-1778
The solvability of certain boundary value problems for a second order ordinary differential equation
p. 1779-1788
On the optimization of control systems in the presence of constraints.~I, II
p. 1789-1800
The solutions of the Briot and Bouquet equation with constant deviations of the argument in the case of simple roots of the characteristic equation
p. 1801-1812
The singular separatrix cycles of a quadratic differential equation that has a straight line as a solution
p. 1813-1818
A certain matrix method in the theory of oscillations
p. 1819-1824
The construction of the differential equations of optimal motion for a given variety
p. 1825-1834
The splitting principle for nonselfadjoint partial differential operators
p. 1835-1844
The generalized localization principle for spectral expansions connected with the Beltrami operator
p. 1845-1853
Boundary value problems for Petrovski{\v\i} well-posed equations of positive genus in the plane
p. 1854-1868
The coefficient stability of the solution of the Dirichlet problem for the equation ${\rm div}\{k(x)\ {\rm grad}\ u\}=-f(x)$
p. 1869-1875
Difference schemes for the solution of ill-posed abstract Cauchy problems
p. 1876-1885
Certain sufficient conditions for stability of the Bubnov-Galerkin method for a boundary value problem in Hilbert space
p. 1886-1894
Stability of linear homogeneous differential equations with delayed argument
p. 1895-1898
The reducibility of a system of two differential equations to normal form
p. 1899-1902
An application of the method of Ljapunov functions to the investigation of oscillations in nonlinear systems with lag
p. 1903-1905
Asymptotic behavior of the solutions of invariant linear systems of differential equations
p. 1906-1910
The first boundary value problem for a charged system of quasi-linear parabolic equations
p. 1911-1913
The extendability of the solutions of equations with delayed argument
p. 1914-1917
The existence and uniqueness of the solution of a certain boundary value problem
p. 1918-1921

Sommaire du Fascicule no. 11

Continuous processes of Newton type
p. 1931-1945
Certain solutions of systems of ordinary differential equations with a polynomial right hand side.~III
p. 1946-1959
The stability in the large of the zero solution of a certain system of three differential equations
p. 1960-1966
The limit cycles of a certain autonomous system
p. 1967-1973
Guaranteeing the accuracy of a signal transmission under constantly acting perturbations
p. 1974-1981
The limit spectrum of systems of first order differential equations with slowly changing coefficients
p. 1982-1991
On the formulation of boundary value problems with infinite defect for differential equations with deviating argument
p. 1992-1997
The asymptotic behavior of the solution of a boundary value problem for an ordinary linear differential equation with small paramater
p. 1998-2006
The closing of the separatrices of a certain first order differential equation
p. 2007-2012
On the question of the existence of the solutions of differential equations with a lag that depends on the solution
p. 2013-2018
The boundedness of the solutions of a second order differential equation with periodic coefficients
p. 2019-2029
Coercive solvability of a boundary-value problem for a second-order elliptic equation in Banach space.~I
p. 2030-2044
A study of the stability of the discontinuous solution of the system of equations of dynamics of a continuous medium that relates to the combustion process of solid fuel charges
p. 2045-2050
The existence of a point of regularity and the spectrum of a second order nonselfadjoint differential operator
p. 2051-2057
The generalized principle of localizing spectral decompositions that are connected with the Beltrami operator given in an arbitrary $n$-dimensional domain
p. 2058-2065
A certain class of singular elliptic operators. I
p. 2066-2077
Estimates for the approximate solution of the Cauchy problem, and the method of lines
p. 2078-2085
An application of characteristic exponents of order $m$ to the study of asymptotic stability
p. 2086-2090
Explicit solutions of certain difference approximations of the heat equation
p. 2091-2093
An estimate of the jump of the highest exponent of invariant linear systems under the action of small perturbations
p. 2094-2098
The solutions of the Briot and Bouquet equation with constant deviations of the argument in the case of multiple roots of the characteristic equation
p. 2099-2102
Asymptotic stability of a certain system of two differential equations
p. 2103-2106
Qualitative investigation in the large of a certain second order system
p. 2107-2110
An asymptotic solution of ordinary second order differential equations
p. 2111-2114
The boundedness of the solutions of linear differential difference equations with variable coefficients in a Banach space
p. 2115-2116
The construction of the switching line in the case of an isochronous family of glued solutions
p. 2117-2119
Поправки к~статье: «Об одном методе построения приближенного решения дифференциальных
Поправки к~статье: «Асимптотические формулы собственных значений эллиптических операторов
Поправки к~статье: «К~вопросу об асимптотическом распределении собственных значений

Sommaire du Fascicule no. 12

Some properties of the solutions of a certain second order equation
p. 2131-2135
The canonical form of a linear two-dimensional system with variable coefficients
p. 2136-2142
Boundary value problems with infinite defect for differential equations with deviating argument
p. 2143-2150
A linear problem of time-optimality in the case of analytic perturbations of the initial conditions
p. 2151-2160
On the problem of the existence of optimal controls
p. 2161-2167
The existence of periodic solutions in linear systems of general form with a distributed deviation of the argument
p. 2168-2175
On the problem of the analytic construction of optimal regulators
p. 2176-2186
A remark on Tihonov's theorem
p. 2187-2190
Coercive solvability of a boundary value problem for a second order elliptic equation in a Banach space. I, II
p. 2191-2198
Generalized kernels of fractional order
p. 2199-2210
Integral estimates of the derivatives of $l$-metaharmonic functions in an $N$-dimensional domain in the $L_p$ metric
p. 2211-2224
A geometric picture of the integral surfaces near a singular integral element of a first order partial differential equation
p. 2225-2233
A multidimensional integral equation with a difference kernel
p. 2234-2239
A certain vector integro-differential equation of elasticity theory
p. 2240-2245
The order of growth of the resolvent kernels of a system of Volterra integral equations with periodic kernels and lags
p. 2246-2252
The existence of a limit as $t\rightarrow \infty $ of the solution of a nonlinear Volterra equation
p. 2253-2258
The solution of integro-differential equations with self-regulating lag
p. 2259-2264
The stability of the zero solution of almost triangular systems of difference equations
p. 2265-2268
The stability of the solution of a linear differential equation with retarded argument
p. 2269-2274
A remark on the existence of an unbounded solution of a second order linear equation
Construction of program controls in certain nonlinear systems
p. 2276-2278
The isochrony of a system of three differential equations in the presence of a family of nonperiodic solutions in the neighborhood of the origin
p. 2279-2282
An upper estimate for the solutions of a nonlinear first order equation of lagging type
p. 2283-2284
The conditions for the center of a certain system of differential equations
p. 2285-2286
Certain properties of the polynomial solutions of higher order differential equations
p. 2287-2289