|
34-XX
|
Ordinary differential equations
|
|
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
|
|
34A25
|
Analytical theory: series, transformations, transforms, operational calculus, etc.
[See also
44-XX]
|
|
34A26
|
Geometric methods in differential equations
|
|
34A30
|
Linear equations and systems
|
|
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
|
|
34A60
|
Differential inclusions
[See also
49J24,
49K24]
|
|
34A99
|
None of the above, but in this section
|
|
34Bxx
|
Boundary value problems
{For ordinary differential operators, see
34Lxx}
|
|
34B05
|
Linear boundary value problems
|
|
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 values 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]
|
|
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]
|
|
34D05
|
Asymptotic properties
|
|
34D08
|
Characteristic and Lyapunov exponents
|
|
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,
37D50]
|
|
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
|
|
34E99
|
None of the above, but in this section
|
|
34F05
|
Equations and systems with randomness
[See also
34K50,
60H10,
93E03]
|
|
34Gxx
|
Differential equations in abstract spaces
[See also
37Kxx,
34Lxx,
47Dxx,
47Hxx,
47Jxx,
58D25]
|
|
34G10
|
Linear equations
[See also
47D06,
47D09]
|
|
34G20
|
Nonlinear equations
[See also
47Hxx,
47Jxx]
|
|
34G25
|
Evolution inclusions
|
|
34G99
|
None of the above, but in this section
|
|
34H05
|
Control problems
[See also
49J25,
49K25,
93C15]
|
|
34Kxx
|
Functional-differential and differential-difference equations
[See also
37-XX]
|
|
34K05
|
General theory
|
|
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]
|
|
34K35
|
Control problems
[See also
49J25,
49K25,
93C15]
|
|
34K40
|
Neutral equations
|
|
34K50
|
Stochastic delay equations
[See also
34F05,
60Hxx]
|
|
34K60
|
Applications
|
|
34K99
|
None of the above, but in this section
|
|
34Lxx
|
Ordinary differential operators
[See also
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
|
|
34L30
|
Nonlinear ordinary differential operators
|
|
34L40
|
Particular operators (Dirac, one-dimensional Schr\"odinger, etc.)
|
|
34L99
|
None of the above, but in this section
|
|
34Mxx
|
Differential equations in the complex domain
[See also
30Dxx,
32G34]
|
|
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
|
|
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
|
Painlev\'e 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
|