| 34-XX | | Prev: 33 | Up: Top | Next: 35 | |
| Ordinary differential equations [xref: 22E05] |
34-00
| General reference works (handbooks, dictionaries, bibliographies, etc.)
| 34-01
| Instructional exposition (textbooks, tutorial papers, etc.)
| 34-02
| Research exposition (monographs, survey articles)
| 34-03
| Historical (must also be assigned at least one classification number from Section 01)
| 34-04
| Explicit machine computation and programs (not the theory of computation or programming)
| 34-06
| Proceedings, conferences, collections, etc.
| |
34Axx
| General theory
| 34A05 |
Explicit solutions and reductions
| 34A09 |
Implicit equations, differential-algebraic equations [See also 65L80]
| 34A12 |
Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions
[xref: 45D05]
| 34A25 |
Analytical theory: series, transformations, transforms, operational calculus, etc. [See also 44-XX]
| 34A26 |
Geometric methods in differential equations
| 34A30 |
Linear equations and systems, general
| 34A34 |
Nonlinear equations and systems, general
| 34A35 |
Differential equations of infinite order
| 34A36 |
Discontinuous equations
| 34A37 |
Differential equations with impulses
| 34A40 |
Differential inequalities [See also 26D20]
| 34A45 |
Theoretical approximation of solutions {For numerical analysis, see 65Lxx}
| 34A55 |
Inverse problems
[xref: 81Uxx]
| 34A60 |
Differential inclusions [See also 49J24, 49K24]
[xref: 49J24, 49K24]
| 34A99 |
None of the above, but in this section
| |
34Bxx
| Boundary value problems {For ordinary differential operators, see 34Lxx}
[xref: 47E05]
| 34B05 |
Linear boundary value problems
| 34B07 |
Linear boundary value problems with nonlinear dependence on the spectral parameter
| 34B08 |
Multi-parameter boundary value problems
| 34B09 |
Boundary value problems with an indefinite weight
| 34B10 |
Multipoint boundary value problems
| 34B15 |
Nonlinear boundary value problems
| 34B16 |
Singular nonlinear boundary value problems
| 34B18 |
Positive solutions of nonlinear boundary value problems
| 34B20 |
Weyl theory and its generalizations
| 34B24 |
Sturm-Liouville theory [See also 34Lxx]
| 34B27 |
Green functions
| 34B30 |
Special equations (Mathieu, Hill, Bessel, etc.)
| 34B37 |
Boundary value problems with impulses
| 34B40 |
Boundary value problems on infinite intervals
| 34B45 |
Boundary value problems on graphs and networks
| 34B60 |
Applications
| 34B99 |
None of the above, but in this section
| |
34Cxx
| Qualitative theory [See also 37-XX]
[xref: 37Cxx, 37Gxx, 70Kxx]
| 34C05 |
Location of integral curves, singular points, limit cycles
| 34C07 |
Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications)
| 34C08 |
Connections with real algebraic geometry (fewnomials, desingularization, zeros of Abelian integrals, etc.)
| 34C10 |
Oscillation theory, zeros, disconjugacy and comparison theory
| 34C11 |
Growth, boundedness, comparison of solutions
| 34C12 |
Monotone systems
| 34C14 |
Symmetries, invariants
| 34C15 |
Nonlinear oscillations, coupled oscillators
| 34C20 |
Transformation and reduction of equations and systems, normal forms
| 34C23 |
Bifurcation [See mainly 37Gxx]
| 34C25 |
Periodic solutions
| 34C26 |
Relaxation oscillations
| 34C27 |
Almost periodic solutions
| 34C28 |
Complex behavior, chaotic systems [See mainly 37Dxx]
| 34C29 |
Averaging method
| 34C30 |
Manifolds of solutions
| 34C37 |
Homoclinic and heteroclinic solutions
| 34C40 |
Equations and systems on manifolds
| 34C41 |
Equivalence, asymptotic equivalence
| 34C45 |
Method of integral manifolds
| 34C55 |
Hysteresis
| 34C60 |
Applications
| 34C99 |
None of the above, but in this section
| |
34Dxx
| Stability theory [See also 37C75, 93Dxx]
[xref: 37Cxx]
| 34D05 |
Asymptotic properties
| 34D08 |
Characteristic and Lyapunov exponents
[xref: 37H15, 37Hxx]
| 34D09 |
Dichotomy, trichotomy
| 34D10 |
Perturbations
| 34D15 |
Singular perturbations
| 34D20 |
Lyapunov stability
| 34D23 |
Global stability
| 34D30 |
Structural stability and analogous concepts [See also 37C20]
| 34D35 |
Stability of manifolds of solutions
| 34D40 |
Ultimate boundedness
| 34D45 |
Attractors [See also 37C70, 37D45]
| 34D99 |
None of the above, but in this section
| |
34Exx
| Asymptotic theory
| 34E05 |
Asymptotic expansions
| 34E10 |
Perturbations, asymptotics
| 34E13 |
Multiple scale methods
| 34E15 |
Singular perturbations, general theory
| 34E18 |
Methods of nonstandard analysis
| 34E20 |
Singular perturbations, turning point theory, WKB methods
[xref: 34M60, 78A45, 81U05]
| 34E99 |
None of the above, but in this section
| |
34F05
| Equations and systems with randomness [See also 34K50, 60H10, 93E03]
[xref: 34K50, 37H10, 37Hxx, 60H10]
| |
34Gxx
| Differential equations in abstract spaces [See also 34Lxx, 37Kxx, 47Dxx, 47Hxx, 47Jxx, 58D25]
[xref: 34K30, 35R20, 58D25]
| 34G10 |
Linear equations [See also 47D06, 47D09]
[xref: 47D06, 47D09]
| 34G20 |
Nonlinear equations [See also 47Hxx, 47Jxx]
[xref: 47J35]
| 34G25 |
Evolution inclusions
| 34G99 |
None of the above, but in this section
| |
34H05
| Control problems [See also 49J25, 49K25, 93C15]
[xref: 93C15]
| |
34Kxx
| Functional-differential and differential-difference equations [See also 37-XX]
| 34K05 |
General theory
[xref: 45J05]
| 34K06 |
Linear functional-differential equations
| 34K07 |
Theoretical approximation of solutions
| 34K10 |
Boundary value problems
| 34K11 |
Oscillation theory
| 34K12 |
Growth, boundedness, comparison of solutions
| 34K13 |
Periodic solutions
| 34K14 |
Almost periodic solutions
| 34K17 |
Transformation and reduction of equations and systems, normal forms
| 34K18 |
Bifurcation theory
| 34K19 |
Invariant manifolds
| 34K20 |
Stability theory
| 34K23 |
Complex (chaotic) behavior of solutions
| 34K25 |
Asymptotic theory
| 34K26 |
Singular perturbations
| 34K28 |
Numerical approximation of solutions
| 34K29 |
Inverse problems
| 34K30 |
Equations in abstract spaces [See also 34Gxx, 47Dxx, 47Hxx]
[xref: 45J05, 45K05, 47D06, 47G20]
| 34K35 |
Control problems [See also 49J25, 49K25, 93C15]
[xref: 49J25, 49K25, 93C23]
| 34K40 |
Neutral equations
| 34K45 |
Equations with impulses
| 34K50 |
Stochastic delay equations [See also 34F05, 60Hxx]
[xref: 34F05, 37H10]
| 34K60 |
Applications
| 34K99 |
None of the above, but in this section
| |
34Lxx
| Ordinary differential operators [See also 47E05]
[xref: 34B24, 34Gxx, 45C05, 47E05]
| 34L05 |
General spectral theory
| 34L10 |
Eigenfunction expansions, completeness of eigenfunctions
| 34L15 |
Estimation of eigenvalues, upper and lower bounds
| 34L16 |
Numerical approximation of eigenvalues and of other parts of the spectrum
| 34L20 |
Asymptotic distribution of eigenvalues, asymptotic theory of eigenfunctions
| 34L25 |
Scattering theory
[xref: 47A40, 81Uxx]
| 34L30 |
Nonlinear ordinary differential operators
| 34L40 |
Particular operators (Dirac, one-dimensional Schrödinger, etc.)
[xref: 81Uxx]
| 34L99 |
None of the above, but in this section
| |
34Mxx
| Differential equations in the complex domain [See also 30Dxx, 32G34]
[xref: 12H20, 30D05, 32G34, 37F75]
| 34M05 |
Entire and meromorphic solutions
| 34M10 |
Oscillation, growth of solutions
| 34M15 |
Algebraic aspects (differential-algebraic, hypertranscendence, group-theoretical)
| 34M20 |
Nonanalytic aspects
| 34M25 |
Formal solutions, transform techniques
| 34M30 |
Asymptotics, summation methods
| 34M35 |
Singularities, monodromy, local behavior of solutions, normal forms
| 34M37 |
Resurgence phenomena
| 34M40 |
Stokes phenomena and connection problems (linear and nonlinear)
| 34M45 |
Differential equations on complex manifolds
| 34M50 |
Inverse problems (Riemann-Hilbert, inverse differential Galois, etc.)
| 34M55 |
Painlevé and other special equations; classification, hierarchies; isomonodromic deformations
| 34M60 |
Singular perturbation problems in the complex domain (complex WKB, turning points, steepest descent) [See also 34E20]
| 34M99 |
None of the above, but in the same section
| |