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Mathematics Subject Classification – MSC2020

General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to ordinary differential equations 44

34-01

Introductory exposition (textbooks, tutorial papers, etc.) pertaining to ordinary differential equations 1593

34-02

Research exposition (monographs, survey articles) pertaining to ordinary differential equations 1306

34-03

History of ordinary differential equations [Consider also classification numbers pertaining to Section 01-XX] 330

34-04

Software, source code, etc. for problems pertaining to ordinary differential equations 583

34-06

Proceedings, conferences, collections, etc. pertaining to ordinary differential equations 1336

34-11

Research data for problems pertaining to ordinary differential equations 0

34Axx

General theory for ordinary differential equations 52228

34A05

Explicit solutions, first integrals of ordinary differential equations 3591

34A06

Generalized ordinary differential equations (measure-differential equations, set-valued differential equations, etc.) 7

34A07

Fuzzy ordinary differential equations 545

34A08

Fractional ordinary differential equations and fractional differential inclusions 6109

34A09

Implicit ordinary differential equations, differential-algebraic equations 1873

34A12

Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations 5740

34A25

Analytical theory of ordinary differential equations: series, transformations, transforms, operational calculus, etc. [See also 44-XX] 3796

34A26

Geometric methods in ordinary differential equations 1008

34A30

Linear ordinary differential equations and systems, general 9549

34A33

Ordinary lattice differential equations 312

34A34

Nonlinear ordinary differential equations and systems, general theory 11370

34A35

Ordinary differential equations of infinite order 479

34A36

Discontinuous ordinary differential equations 1257

34A37

Ordinary differential equations with impulses 3275

34A38

Hybrid systems of ordinary differential equations 158

34A40

Differential inequalities involving functions of a single real variable [See also 26D20] 1251

34A45

Theoretical approximation of solutions to ordinary differential equations {For numerical analysis, see 65Lxx} 3650

34A55

Inverse problems involving ordinary differential equations 2502

34A60

Ordinary differential inclusions [See also 49J21, 49K21] 3488

34A99

None of the above, but in this section 1428

34Bxx

Boundary value problems for ordinary differential equations {For ordinary differential operators, see 34Lxx} 31771

34B05

Linear boundary value problems for ordinary differential equations 4639

34B07

Linear boundary value problems for ordinary differential equations with nonlinear dependence on the spectral parameter 165

34B08

Parameter dependent boundary value problems for ordinary differential equations 575

34B09

Boundary eigenvalue problems for ordinary differential equations 1057

34B10

Nonlocal and multipoint boundary value problems for ordinary differential equations 5118

34B15

Nonlinear boundary value problems for ordinary differential equations 13567

34B16

Singular nonlinear boundary value problems for ordinary differential equations 2277

34B18

Positive solutions to nonlinear boundary value problems for ordinary differential equations 4747

34B20

Weyl theory and its generalizations for ordinary differential equations 842

34B24

Sturm-Liouville theory [See also 34Lxx] 3602

34B27

Green’s functions for ordinary differential equations 1693

34B30

Special ordinary differential equations (Mathieu, Hill, Bessel, etc.) 1399

34B37

Boundary value problems with impulses for ordinary differential equations 886

34B40

Boundary value problems on infinite intervals for ordinary differential equations 1114

34B45

Boundary value problems on graphs and networks for ordinary differential equations 632

34B60

Applications of boundary value problems involving ordinary differential equations 214

34B99

None of the above, but in this section 523

34Cxx

Qualitative theory for ordinary differential equations [See also 37-XX] 53333

34C05

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations 8552

34C07

Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert’s 16th problem and ramifications) for ordinary differential equations 1501

34C08

Ordinary differential equations and connections with real algebraic geometry (fewnomials, desingularization, zeros of abelian integrals, etc.) 355

34C10

Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations 7083

34C11

Growth and boundedness of solutions to ordinary differential equations 3407

34C12

Monotone systems involving ordinary differential equations 199

34C14

Symmetries, invariants of ordinary differential equations [See also 37C79] 1668

34C15

Nonlinear oscillations and coupled oscillators for ordinary differential equations 5853

34C20

Transformation and reduction of ordinary differential equations and systems, normal forms 3360

34C23

Bifurcation theory for ordinary differential equations [See also 37Gxx] 7259

34C25

Periodic solutions to ordinary differential equations 12555

34C26

Relaxation oscillations for ordinary differential equations 261

34C27

Almost and pseudo-almost periodic solutions to ordinary differential equations 1791

34C28

Complex behavior and chaotic systems of ordinary differential equations [See also 37Dxx] 3032

34C29

Averaging method for ordinary differential equations 1663

34C37

Homoclinic and heteroclinic solutions to ordinary differential equations 2595

34C40

Ordinary differential equations and systems on manifolds 680

34C41

Equivalence and asymptotic equivalence of ordinary differential equations 279

34C45

Invariant manifolds for ordinary differential equations 1029

34C46

Multifrequency systems of ordinary differential equations 109

34C55

Hysteresis for ordinary differential equations 247

34C60

Qualitative investigation and simulation of ordinary differential equation models 5698

34C99

None of the above, but in this section 922

34Dxx

Stability theory for ordinary differential equations [See also 37C75, 93Dxx] 27584

34D05

Asymptotic properties of solutions to ordinary differential equations 6655

34D06

Synchronization of solutions to ordinary differential equations 2624

34D08

Characteristic and Lyapunov exponents of ordinary differential equations 1202

34D09

Dichotomy, trichotomy of solutions to ordinary differential equations 618

34D10

Perturbations of ordinary differential equations 2178

34D15

Singular perturbations of ordinary differential equations 942

34D20

Stability of solutions to ordinary differential equations 11184

34D23

Global stability of solutions to ordinary differential equations 2629

34D30

Structural stability and analogous concepts of solutions to ordinary differential equations [See also 37C20] 978

34D35

Stability of manifolds of solutions to ordinary differential equations 422

34D45

Attractors of solutions to ordinary differential equations [See also 37C70, 37D45] 1384

34D99

None of the above, but in this section 1195

34Exx

Asymptotic theory for ordinary differential equations 10841

34E05

Asymptotic expansions of solutions to ordinary differential equations 3461

34E10

Perturbations, asymptotics of solutions to ordinary differential equations 1778

34E13

Multiple scale methods for ordinary differential equations 844

34E15

Singular perturbations, general theory for ordinary differential equations 4385

34E17

Canard solutions to ordinary differential equations 149

34E18

Methods of nonstandard analysis for ordinary differential equations 44

34E20

Singular perturbations, turning point theory, WKB methods for ordinary differential equations 1435

34E99

None of the above, but in this section 385

34Fxx

Ordinary differential equations and systems with randomness [See also 34K50, 60H10, 93E03] 3964

34F05

Ordinary differential equations and systems with randomness [See also 34K50, 60H10, 93E03] 3831

34F10

Bifurcation of solutions to ordinary differential equations involving randomness 67

34F15

Resonance phenomena for ordinary differential equations involving randomness 109

34F99

None of the above, but in this section 2

34Gxx

Differential equations in abstract spaces [See also 34Lxx, 37Kxx, 47Dxx, 47Hxx, 47Jxx, 58D25] 10887

34G10

Linear differential equations in abstract spaces [See also 47D06, 47D09] 4011

34G20

Nonlinear differential equations in abstract spaces [See also 47Hxx, 47Jxx] 4550

34G25

Evolution inclusions 996

34G99

None of the above, but in this section 1492

34Hxx

Control problems including ordinary differential equations [See also 49J15, 49K15, 93C15] 5078

34H05

Control problems involving ordinary differential equations [See also 49J15, 49K15, 93C15] 3263

34H10

Chaos control for problems involving ordinary differential equations 1611

34H15

Stabilization of solutions to ordinary differential equations 210

34H20

Bifurcation control of ordinary differential equations 114

34H99

None of the above, but in this section 8

34Kxx

Functional-differential equations (including equations with delayed, advanced or state-dependent argument) 33154

34K04

Symmetries, invariants of functional-differential equations [See also 37C79] 1

34K05

General theory of functional-differential equations 3312

34K06

Linear functional-differential equations 1447

34K07

Theoretical approximation of solutions to functional-differential equations 448

34K08

Spectral theory of functional-differential operators 139

34K09

Functional-differential inclusions 266

34K10

Boundary value problems for functional-differential equations 2372

34K11

Oscillation theory of functional-differential equations 2668

34K12

Growth, boundedness, comparison of solutions to functional-differential equations [See also 37C35] 863

34K13

Periodic solutions to functional-differential equations [See also 37C27] 3755

34K14

Almost and pseudo-almost periodic solutions to functional-differential equations 809

34K16

Heteroclinic and homoclinic orbits of functional-differential equations [See also 37C29] 5

34K17

Transformation and reduction of functional-differential equations and systems, normal forms 456

34K18

Bifurcation theory of functional-differential equations [See also 37Gxx] 1856

34K19

Invariant manifolds of functional-differential equations 431

34K20

Stability theory of functional-differential equations [See also 37C75] 9208

34K21

Stationary solutions of functional-differential equations 241

34K23

Complex (chaotic) behavior of solutions to functional-differential equations [See also 37D45] 298

34K24

Synchronization of functional-differential equations 6

34K25

Asymptotic theory of functional-differential equations 3011

34K26

Singular perturbations of functional-differential equations 357

34K27

Perturbations of functional-differential equations 140

34K29

Inverse problems for functional-differential equations 127

34K30

Functional-differential equations in abstract spaces [See also 34Gxx, 35R09, 35R10, 47Jxx] 2254

34K31

Lattice functional-differential equations 113

34K32

Implicit functional-differential equations 90

34K33

Averaging for functional-differential equations 73

34K34

Hybrid systems of functional-differential equations 57

34K35

Control problems for functional-differential equations [See also 49J21, 49K21, 93C23] 2650

34K36

Fuzzy functional-differential equations 151

34K37

Functional-differential equations with fractional derivatives 1033

34K38

Functional-differential inequalities 111

34K39

Discontinuous functional-differential equations 9

34K40

Neutral functional-differential equations 4061

34K41

Functional-differential equations in the complex domain 3

34K42

Functional-differential equations on time scales or measure chains 1

34K43

Functional-differential equations with state-dependent arguments 3

34K45

Functional-differential equations with impulses 2043

34K50

Stochastic functional-differential equations [See also 34Fxx, 60Hxx] 1585

34K60

Qualitative investigation and simulation of models involving functional-differential equations 2959

34K99

None of the above, but in this section 3413

34Lxx

Ordinary differential operators [See also 47E05] 12940

34L05

General spectral theory of ordinary differential operators 2178

34L10

Eigenfunctions, eigenfunction expansions, completeness of eigenfunctions of ordinary differential operators 1450

34L15

Eigenvalues, estimation of eigenvalues, upper and lower bounds of ordinary differential operators 1727

34L16

Numerical approximation of eigenvalues and of other parts of the spectrum of ordinary differential operators 492

34L20

Asymptotic distribution of eigenvalues, asymptotic theory of eigenfunctions for ordinary differential operators 1035

34L25

Scattering theory, inverse scattering involving ordinary differential operators 730

34L30

Nonlinear ordinary differential operators 396

34L40

Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) 3543

34L99

None of the above, but in this section 3711

34Mxx

Ordinary differential equations in the complex domain [See also 30Dxx, 32G34] 6812

34M03

Linear ordinary differential equations and systems in the complex domain 470

34M04

Nonlinear ordinary differential equations and systems in the complex domain 2

34M05

Entire and meromorphic solutions to ordinary differential equations in the complex domain 870

34M10

Oscillation, growth of solutions to ordinary differential equations in the complex domain 716

34M15

Algebraic aspects (differential-algebraic, hypertranscendence, group-theoretical) of ordinary differential equations in the complex domain 314

34M25

Formal solutions and transform techniques for ordinary differential equations in the complex domain 239

34M30

Asymptotics and summation methods for ordinary differential equations in the complex domain 201

34M35

Singularities, monodromy and local behavior of solutions to ordinary differential equations in the complex domain, normal forms 923

34M40

Stokes phenomena and connection problems (linear and nonlinear) for ordinary differential equations in the complex domain 297

34M45

Ordinary differential equations on complex manifolds 109

34M46

Spectral theory for ordinary differential operators in the complex domain 1

34M50

Inverse problems (Riemann-Hilbert, inverse differential Galois, etc.) for ordinary differential equations in the complex domain 234

34M55

Painlevé and other special ordinary differential equations in the complex domain; classification, hierarchies 1753

34M56

Isomonodromic deformations for ordinary differential equations in the complex domain 155

34M60

Singular perturbation problems for ordinary differential equations in the complex domain (complex WKB, turning points, steepest descent) [See also 34E20] 234

34M65

Topological structure of trajectories of ordinary differential equations in the complex domain 0

34M99

None of the above, but in this section 1864

34Nxx

Dynamic equations on time scales or measure chains {For real analysis on time scales, see 26E70} 1596

34N05

Dynamic equations on time scales or measure chains {For real analysis on time scales or measure chains, see 26E70} 1589

34N99

None of the above, but in this section 7

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Mathematics Subject Classification – MSC2020

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