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Mathematics Subject Classification – MSC2010

34-XX

Ordinary differential equations 171704

34-00

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

34-01

Instructional exposition (textbooks, tutorial papers, etc.) 1508

34-02

Research exposition (monographs, survey articles) 1246

34-03

Historical (must also be assigned at least one classification number from Section 01) 321

34-04

Explicit machine computation and programs (not the theory of computation or programming) 568

34-06

Proceedings, conferences, collections, etc. 1290

34Axx

General theory 48361

34A05

Explicit solutions and reductions 3377

34A07

Fuzzy differential equations 407

34A08

Fractional differential equations 4290

34A09

Implicit equations, differential-algebraic equations [See also 65L80] 1782

34A12

Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions 5446

34A25

Analytical theory: series, transformations, transforms, operational calculus, etc. [See also 44-XX] 3677

34A26

Geometric methods in differential equations 966

34A30

Linear equations and systems, general 9336

34A33

Lattice differential equations 244

34A34

Nonlinear equations and systems, general 10981

34A35

Differential equations of infinite order 474

34A36

Discontinuous equations 1069

34A37

Differential equations with impulses 2920

34A38

Hybrid systems 127

34A40

Differential inequalities [See also 26D20] 1208

34A45

Theoretical approximation of solutions [For numerical analysis, see 65Lxx] 3406

34A55

Inverse problems 2341

34A60

Differential inclusions [See also 49J21, 49K21] 3308

34A99

None of the above, but in this section 1420

34Bxx

Boundary value problems [For ordinary differential operators, see 34Lxx] 29842

34B05

Linear boundary value problems 4511

34B07

Linear boundary value problems with nonlinear dependence on the spectral parameter 152

34B08

Parameter dependent boundary value problems 480

34B09

Boundary eigenvalue problems 841

34B10

Nonlocal and multipoint boundary value problems 4707

34B15

Nonlinear boundary value problems 12954

34B16

Singular nonlinear boundary value problems 2134

34B18

Positive solutions of nonlinear boundary value problems 4334

34B20

Weyl theory and its generalizations 804

34B24

Sturm-Liouville theory [See also 34Lxx] 3335

34B27

Green functions 1534

34B30

Special equations (Mathieu, Hill, Bessel, etc.) 1355

34B37

Boundary value problems with impulses 775

34B40

Boundary value problems on infinite intervals 1017

34B45

Boundary value problems on graphs and networks 523

34B60

Applications 189

34B99

None of the above, but in this section 514

34Cxx

Qualitative theory [See also 37-XX] 49928

34C05

Location of integral curves, singular points, limit cycles 7994

34C07

Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert’s 16th problem and ramifications) 1318

34C08

Connections with real algebraic geometry (fewnomials, desingularization, zeros of Abelian integrals, etc.) 318

34C10

Oscillation theory, zeros, disconjugacy and comparison theory 6908

34C11

Growth, boundedness 3310

34C12

Monotone systems 183

34C14

Symmetries, invariants 1493

34C15

Nonlinear oscillations, coupled oscillators 5378

34C20

Transformation and reduction of equations and systems, normal forms 3197

34C23

Bifurcation [See also 37Gxx] 6395

34C25

Periodic solutions 11980

34C26

Relaxation oscillations 225

34C27

Almost and pseudo-almost periodic solutions 1713

34C28

Complex behavior, chaotic systems [See also 37Dxx] 2695

34C29

Averaging method 1600

34C37

Homoclinic and heteroclinic solutions 2424

34C40

Equations and systems on manifolds 643

34C41

Equivalence, asymptotic equivalence 264

34C45

Invariant manifolds 912

34C46

Multifrequency systems 99

34C55

Hysteresis 230

34C60

Qualitative investigation and simulation of models 4917

34C99

None of the above, but in this section 918

34Dxx

Stability theory [See also 37C75, 93Dxx] 25133

34D05

Asymptotic properties 6231

34D06

Synchronization 2031

34D08

Characteristic and Lyapunov exponents 1114

34D09

Dichotomy, trichotomy 569

34D10

Perturbations 2068

34D15

Singular perturbations 913

34D20

Stability 10328

34D23

Global stability 2143

34D30

Structural stability and analogous concepts [See also 37C20] 958

34D35

Stability of manifolds of solutions 401

34D45

Attractors [See also 37C70, 37D45] 1273

34D99

None of the above, but in this section 1192

34Exx

Asymptotic theory 10447

34E05

Asymptotic expansions 3365

34E10

Perturbations, asymptotics 1643

34E13

Multiple scale methods 809

34E15

Singular perturbations, general theory 4242

34E17

Canard solutions 123

34E18

Methods of nonstandard analysis 42

34E20

Singular perturbations, turning point theory, WKB methods 1401

34E99

None of the above, but in this section 384

34Fxx

Equations and systems with randomness [See also 34K50, 60H10, 93E03] 3528

34F05

Equations and systems with randomness [See also 34K50, 60H10, 93E03] 3422

34F10

Bifurcation 55

34F15

Resonance phenomena 85

34F99

None of the above, but in this section 2

34Gxx

Differential equations in abstract spaces [See also 34Lxx, 37Kxx, 47Dxx, 47Hxx, 47Jxx, 58D25] 10525

34G10

Linear equations [See also 47D06, 47D09] 3902

34G20

Nonlinear equations [See also 47Hxx, 47Jxx] 4376

34G25

Evolution inclusions 919

34G99

None of the above, but in this section 1491

34Hxx

Control problems [See also 49J15, 49K15, 93C15] 4569

34H05

Control problems [See also 49J15, 49K15, 93C15] 3091

34H10

Chaos control 1334

34H15

Stabilization 162

34H20

Bifurcation control 93

34H99

None of the above, but in this section 8

34Kxx

Functional-differential and differential-difference equations [See also 37-XX] 30617

34K05

General theory 3244

34K06

Linear functional-differential equations 1303

34K07

Theoretical approximation of solutions 386

34K08

Spectral theory of functional-differential operators 97

34K09

Functional-differential inclusions 214

34K10

Boundary value problems 2255

34K11

Oscillation theory 2455

34K12

Growth, boundedness, comparison of solutions 788

34K13

Periodic solutions 3426

34K14

Almost and pseudo-periodic solutions 737

34K17

Transformation and reduction of equations and systems, normal forms 410

34K18

Bifurcation theory 1598

34K19

Invariant manifolds 383

34K20

Stability theory 8318

34K21

Stationary solutions 174

34K23

Complex (chaotic) behavior of solutions 256

34K25

Asymptotic theory 2774

34K26

Singular perturbations 318

34K27

Perturbations 107

34K28

Numerical approximation of solutions 1030

34K29

Inverse problems 102

34K30

Equations in abstract spaces [See also 34Gxx, 35R09, 35R10, 47Jxx] 2034

34K31

Lattice functional-differential equations 99

34K32

Implicit equations 68

34K33

Averaging 62

34K34

Hybrid systems 34

34K35

Control problems [See also 49J21, 49K21, 93C23] 2519

34K36

Fuzzy functional-differential equations 108

34K37

Functional-differential equations with fractional derivatives 701

34K38

Functional-differential inequalities 97

34K40

Neutral equations 3754

34K45

Equations with impulses 1817

34K50

Stochastic functional-differential equations [See also 34Fxx, 60Hxx] 1316

34K60

Qualitative investigation and simulation of models 2617

34K99

None of the above, but in this section 3410

34Lxx

Ordinary differential operators [See also 47E05] 12295

34L05

General spectral theory 2017

34L10

Eigenfunctions, eigenfunction expansions, completeness of eigenfunctions 1297

34L15

Eigenvalues, estimation of eigenvalues, upper and lower bounds 1578

34L16

Numerical approximation of eigenvalues and of other parts of the spectrum 462

34L20

Asymptotic distribution of eigenvalues, asymptotic theory of eigenfunctions 955

34L25

Scattering theory, inverse scattering 692

34L30

Nonlinear ordinary differential operators 368

34L40

Particular operators (Dirac, one-dimensional Schrödinger, etc.) 3325

34L99

None of the above, but in this section 3717

34Mxx

Differential equations in the complex domain [See also 30Dxx, 32G34] 6399

34M03

Linear equations and systems 382

34M05

Entire and meromorphic solutions 799

34M10

Oscillation, growth of solutions 664

34M15

Algebraic aspects (differential-algebraic, hypertranscendence, group-theoretical) 288

34M25

Formal solutions, transform techniques 216

34M30

Asymptotics, summation methods 194

34M35

Singularities, monodromy, local behavior of solutions, normal forms 865

34M40

Stokes phenomena and connection problems (linear and nonlinear) 266

34M45

Differential equations on complex manifolds 102

34M50

Inverse problems (Riemann-Hilbert, inverse differential Galois, etc.) 220

34M55

Painlevé and other special equations; classification, hierarchies; 1595

34M56

Isomonodromic deformations 116

34M60

Singular perturbation problems in the complex domain (complex WKB, turning points, steepest descent) [See also 34E20] 216

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] 1353

34N05

Dynamic equations on time scales or measure chains [For real analysis on time scales or measure chains, see 26E70] 1346

34N99

None of the above, but in this section 6

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Mathematics Subject Classification – MSC2010

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