Euler-Lagrange equation


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Euler-Lagrange equation

[¦ȯi·lər lə′grānj i‚kwā·zhən]
(mathematics)
A partial differential equation arising in the calculus of variations, which provides a necessary condition that y (x) minimize the integral over some finite interval of f (x,y,y ′) dx, where y ′ = dy/dx; the equation is (δƒ(x,y,y ′)/δ y) - (d/dx)(δƒ(x,y,y ′)/δ y ′) =0. Also known as Euler's equation.
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Euler-Lagrange equation with first order constraint [[PHI].
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Then the solution of the problem (2) satisfies the following Euler-Lagrange equation
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We provide a growth condition on L to guarantee that u is locally bounded and, by building suitable variations, we prove the validity of the Euler-Lagrange equation without imposing differentiability on L.
The validity of the Euler-Lagrange equation for solutions to variational functionals with fast growth
Equation (58) is just the well-known Euler-Lagrange equation for this system.
The dynamic and collision features of microscopic particles described by the nonlinear Schrodinger equation in the nonlinear quantum systems
This equation can be derived as the Euler-Lagrange equation for the minimization problem:
An area minimizing scheme for anisotropic mean curvature flow
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x] verifies the Euler-Lagrange equation (see [6]), we get
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Topics increase in mathematical complexity as the book progresses to encompass dozens of examples including a derivation of the Euler-Lagrange equation, heat flow and analytic functions, and a bicycle wheel and the Gauss-Bonnet theorem.
The Mathematical Mechanic
The Euler-Lagrange equation tells us that on the turnpike the marginal product of capital must match the rate of change in the valuation of investment.
On optimal growth when there are many goods and factors

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