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Mathematics Subject Classification – MSC2010

34-XX

Ordinary differential equations 170282

34-00

General reference works (handbooks, dictionaries, bibliographies, etc.) 41

34-01

Instructional exposition (textbooks, tutorial papers, etc.) 1501

34-02

Research exposition (monographs, survey articles) 1234

34-03

Historical (must also be assigned at least one classification number from Section 01) 319

34-04

Explicit machine computation and programs (not the theory of computation or programming) 565

34-06

Proceedings, conferences, collections, etc. 1290

34Axx

General theory 47964

34A05

Explicit solutions and reductions 3356

34A07

Fuzzy differential equations 391

34A08

Fractional differential equations 4137

34A09

Implicit equations, differential-algebraic equations [See also 65L80] 1769

34A12

Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions 5409

34A25

Analytical theory: series, transformations, transforms, operational calculus, etc. [See also 44-XX] 3669

34A26

Geometric methods in differential equations 956

34A30

Linear equations and systems, general 9310

34A33

Lattice differential equations 232

34A34

Nonlinear equations and systems, general 10941

34A35

Differential equations of infinite order 472

34A36

Discontinuous equations 1043

34A37

Differential equations with impulses 2877

34A38

Hybrid systems 121

34A40

Differential inequalities [See also 26D20] 1202

34A45

Theoretical approximation of solutions [For numerical analysis, see 65Lxx] 3380

34A55

Inverse problems 2334

34A60

Differential inclusions [See also 49J21, 49K21] 3278

34A99

None of the above, but in this section 1420

34Bxx

Boundary value problems [For ordinary differential operators, see 34Lxx] 29664

34B05

Linear boundary value problems 4508

34B07

Linear boundary value problems with nonlinear dependence on the spectral parameter 150

34B08

Parameter dependent boundary value problems 471

34B09

Boundary eigenvalue problems 830

34B10

Nonlocal and multipoint boundary value problems 4666

34B15

Nonlinear boundary value problems 12900

34B16

Singular nonlinear boundary value problems 2120

34B18

Positive solutions of nonlinear boundary value problems 4298

34B20

Weyl theory and its generalizations 800

34B24

Sturm-Liouville theory [See also 34Lxx] 3313

34B27

Green functions 1519

34B30

Special equations (Mathieu, Hill, Bessel, etc.) 1351

34B37

Boundary value problems with impulses 765

34B40

Boundary value problems on infinite intervals 1003

34B45

Boundary value problems on graphs and networks 510

34B60

Applications 188

34B99

None of the above, but in this section 513

34Cxx

Qualitative theory [See also 37-XX] 49586

34C05

Location of integral curves, singular points, limit cycles 7944

34C07

Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert’s 16th problem and ramifications) 1298

34C08

Connections with real algebraic geometry (fewnomials, desingularization, zeros of Abelian integrals, etc.) 313

34C10

Oscillation theory, zeros, disconjugacy and comparison theory 6886

34C11

Growth, boundedness 3300

34C12

Monotone systems 179

34C14

Symmetries, invariants 1468

34C15

Nonlinear oscillations, coupled oscillators 5321

34C20

Transformation and reduction of equations and systems, normal forms 3182

34C23

Bifurcation [See also 37Gxx] 6342

34C25

Periodic solutions 11918

34C26

Relaxation oscillations 218

34C27

Almost and pseudo-almost periodic solutions 1703

34C28

Complex behavior, chaotic systems [See also 37Dxx] 2663

34C29

Averaging method 1590

34C37

Homoclinic and heteroclinic solutions 2408

34C40

Equations and systems on manifolds 642

34C41

Equivalence, asymptotic equivalence 262

34C45

Invariant manifolds 897

34C46

Multifrequency systems 96

34C55

Hysteresis 225

34C60

Qualitative investigation and simulation of models 4848

34C99

None of the above, but in this section 915

34Dxx

Stability theory [See also 37C75, 93Dxx] 24840

34D05

Asymptotic properties 6196

34D06

Synchronization 1956

34D08

Characteristic and Lyapunov exponents 1106

34D09

Dichotomy, trichotomy 558

34D10

Perturbations 2058

34D15

Singular perturbations 909

34D20

Stability 10225

34D23

Global stability 2081

34D30

Structural stability and analogous concepts [See also 37C20] 957

34D35

Stability of manifolds of solutions 399

34D45

Attractors [See also 37C70, 37D45] 1261

34D99

None of the above, but in this section 1190

34Exx

Asymptotic theory 10410

34E05

Asymptotic expansions 3354

34E10

Perturbations, asymptotics 1638

34E13

Multiple scale methods 804

34E15

Singular perturbations, general theory 4222

34E17

Canard solutions 120

34E18

Methods of nonstandard analysis 42

34E20

Singular perturbations, turning point theory, WKB methods 1399

34E99

None of the above, but in this section 384

34Fxx

Equations and systems with randomness [See also 34K50, 60H10, 93E03] 3478

34F05

Equations and systems with randomness [See also 34K50, 60H10, 93E03] 3381

34F10

Bifurcation 54

34F15

Resonance phenomena 77

34F99

None of the above, but in this section 2

34Gxx

Differential equations in abstract spaces [See also 34Lxx, 37Kxx, 47Dxx, 47Hxx, 47Jxx, 58D25] 10494

34G10

Linear equations [See also 47D06, 47D09] 3887

34G20

Nonlinear equations [See also 47Hxx, 47Jxx] 4368

34G25

Evolution inclusions 910

34G99

None of the above, but in this section 1491

34Hxx

Control problems [See also 49J15, 49K15, 93C15] 4475

34H05

Control problems [See also 49J15, 49K15, 93C15] 3065

34H10

Chaos control 1273

34H15

Stabilization 160

34H20

Bifurcation control 87

34H99

None of the above, but in this section 8

34Kxx

Functional-differential and differential-difference equations [See also 37-XX] 30352

34K05

General theory 3231

34K06

Linear functional-differential equations 1286

34K07

Theoretical approximation of solutions 377

34K08

Spectral theory of functional-differential operators 96

34K09

Functional-differential inclusions 213

34K10

Boundary value problems 2240

34K11

Oscillation theory 2430

34K12

Growth, boundedness, comparison of solutions 781

34K13

Periodic solutions 3395

34K14

Almost and pseudo-periodic solutions 729

34K17

Transformation and reduction of equations and systems, normal forms 408

34K18

Bifurcation theory 1576

34K19

Invariant manifolds 381

34K20

Stability theory 8244

34K21

Stationary solutions 172

34K23

Complex (chaotic) behavior of solutions 251

34K25

Asymptotic theory 2754

34K26

Singular perturbations 315

34K27

Perturbations 105

34K28

Numerical approximation of solutions 1022

34K29

Inverse problems 99

34K30

Equations in abstract spaces [See also 34Gxx, 35R09, 35R10, 47Jxx] 2013

34K31

Lattice functional-differential equations 94

34K32

Implicit equations 68

34K33

Averaging 60

34K34

Hybrid systems 33

34K35

Control problems [See also 49J21, 49K21, 93C23] 2499

34K36

Fuzzy functional-differential equations 103

34K37

Functional-differential equations with fractional derivatives 683

34K38

Functional-differential inequalities 96

34K40

Neutral equations 3738

34K45

Equations with impulses 1798

34K50

Stochastic functional-differential equations [See also 34Fxx, 60Hxx] 1294

34K60

Qualitative investigation and simulation of models 2594

34K99

None of the above, but in this section 3409

34Lxx

Ordinary differential operators [See also 47E05] 12236

34L05

General spectral theory 2014

34L10

Eigenfunctions, eigenfunction expansions, completeness of eigenfunctions 1291

34L15

Eigenvalues, estimation of eigenvalues, upper and lower bounds 1561

34L16

Numerical approximation of eigenvalues and of other parts of the spectrum 453

34L20

Asymptotic distribution of eigenvalues, asymptotic theory of eigenfunctions 948

34L25

Scattering theory, inverse scattering 687

34L30

Nonlinear ordinary differential operators 365

34L40

Particular operators (Dirac, one-dimensional Schrödinger, etc.) 3303

34L99

None of the above, but in this section 3716

34Mxx

Differential equations in the complex domain [See also 30Dxx, 32G34] 6363

34M03

Linear equations and systems 373

34M05

Entire and meromorphic solutions 788

34M10

Oscillation, growth of solutions 658

34M15

Algebraic aspects (differential-algebraic, hypertranscendence, group-theoretical) 285

34M25

Formal solutions, transform techniques 216

34M30

Asymptotics, summation methods 192

34M35

Singularities, monodromy, local behavior of solutions, normal forms 858

34M40

Stokes phenomena and connection problems (linear and nonlinear) 265

34M45

Differential equations on complex manifolds 102

34M50

Inverse problems (Riemann-Hilbert, inverse differential Galois, etc.) 215

34M55

Painlevé and other special equations; classification, hierarchies; 1588

34M56

Isomonodromic deformations 113

34M60

Singular perturbation problems in the complex domain (complex WKB, turning points, steepest descent) [See also 34E20] 215

34M99

None of the above, but in this section 1852

34Nxx

Dynamic equations on time scales or measure chains [For real analysis on time scales see 26E70] 1332

34N05

Dynamic equations on time scales or measure chains [For real analysis on time scales or measure chains, see 26E70] 1325

34N99

None of the above, but in this section 6

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Mathematics Subject Classification – MSC2010

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