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Examples of differential equations; Autonomous system (mathematics) Picard–Lindelöf theorem; Peano existence theorem; Carathéodory existence theorem; Numerical ordinary differential equations; Bendixson–Dulac theorem; Gradient conjecture; Recurrence plot; Limit cycle; Initial value problem; Clairaut's equation; Singular solution ...
Dupire equation (local volatility) Hamilton–Jacobi–Bellman equation. Merton's portfolio problem; Optimal stopping; Malthusian growth model; Mean field game theory [10] Optimal rotation age; Sovereign debt accumulation ˙ = + () Stochastic differential equation. Geometric Brownian motion; Ornstein–Uhlenbeck process
In mathematics, an ordinary differential equation (ODE) is a differential equation (DE) dependent on only a single independent variable. As with any other DE, its unknown(s) consists of one (or more) function (s) and involves the derivatives of those functions. [ 1 ]
The Lorenz attractor is difficult to analyze, but the action of the differential equation on the attractor is described by a fairly simple geometric model. [24] Proving that this is indeed the case is the fourteenth problem on the list of Smale's problems. This problem was the first one to be resolved, by Warwick Tucker in 2002. [25]
Differential equations are prominent in many scientific areas. Nonlinear ones are of particular interest for their commonality in describing real-world systems and how much more difficult they are to solve compared to linear differential equations.
Lagrange's identity (boundary value problem) Lane–Emden equation; Laser diode rate equations; Legendre's differential equation; Libroadrunner; Liénard equation; Liñán's equation; Liouville's formula; Lommel function; Lotka–Volterra equations; Lumped parameter model for the cardiovascular system
Peano existence theorem (ordinary differential equations) Peeling theorem ; Peetre theorem (functional analysis) Peixoto's theorem (dynamical systems) Penrose–Hawking singularity theorems ; Pentagonal number theorem (number theory) Perfect graph theorem (graph theory) Perlis theorem (graph theory) Perpendicular axis theorem
20. The general problem of boundary values (Boundary value problems in PD) 21. Proof of the existence of linear differential equations having a prescribed monodromy group. 22. Uniformization of analytic relations by means of automorphic functions. 23. Further development of the methods of the calculus of variations.