Differential Equations

a dynamical system is the description of how a system evolves in time

Since we don't even know whether these solutions exist, our understanding is at a very primitive level. Standard methods from PDE appear inadequate to settle the problem.

allows one to bound a function that is known to satisfy a certain differential or integral inequality

integral relation satisfied by stationary localized solutions to a nonlinear Schrödinger equation or nonlinear Klein-Gordon equation

Papers of 1836 - 1837 by Sturm and Liouville on differential equations involved expansions of functions in series

In the theory of ordinary differential equations (ODEs), Lyapunov functions, named after Aleksandr Lyapunov, are scalar functions

tence and uniqueness theorem for analytic partial differential equations associated with Cauchy initial value problems.

Kac, establishes a link between parabolic partial differential equations and stochastic processes.

differential equations

differential equations

partial differential equations

partial differential operators

worked on differential equations and singularity theory

He made numerous contributions to differential equations and partial differential equations

Other topics included optics, calculus, trigonometry and partial differential equations in mathematics. == See also == Cotes's spiral == References == == External links == Samuel Earnshaw Archived 12 April 2016 at the Wayback Machine

He was awarded the Fields Medal in 2006 for his contributions to partial differential equations, combinatorics, harmonic analysis, and additive number theory.

In mathematics, the Grothendieck-Katz p-curvature conjecture is a local-global principle for linear ordinary differential equations, related to differential Galois theory and in a loose sense analogous to the result in the Chebotarev density theorem considered as the polynomial case.

The Duffing equation (or Duffing oscillator), named after Georg Duffing (1861-1944), is a non-linear second-order differential equation used to model certain damped and driven oscillators.

In fact, the Airy equation is the simplest second-order linear differential equation with a turning point (a point where the character of the solutions changes from oscillatory to exponential).

They are often employed in solving partial differential equations in many scientific fields.

In mathematics, a Lamé function, or ellipsoidal harmonic function, is a solution of Lamé's equation, a second-order ordinary differential equation.

From the parabolic partial differential equation in the model, known as the Black-Scholes equation, one can deduce the Black-Scholes formula, which gives a theoretical estimate of the price of European-style options and shows that the option has a unique price given the risk of the security and its expected return (instead replacing the security's expected return with the risk-neutral rate).

In mathematics, Abel's identity (also called Abel's formula or Abel's differential equation identity) is an equation that expresses the Wronskian of two solutions of a homogeneous second-order linear ordinary differential equation in terms of a coefficient of the original differential equation.

Calculus and Analysis Differential Equations

Calculus and Analysis Differential Equations

Kurt Friedrichs was a German American mathematician who worked on many aspects of partial differential equations.

Marcel Riesz was a Hungarian-born mathematician who worked on summation methods, potential theory and other parts of analysis, as well as number theory and partial differential equations.

Sergei Bernstein was a Ukrainian mathematician who made important contributions to partial differential equations, differential geometry, probability theory and approximation theory.

Vladimir Arnold is a Ukrainian-born mathematician who won a Wolf prize for his work on dynamical systems, differential equations and singularity theory.