The purpose of this paper is to discuss the forms of the Euler-Lagrange equations.The polynomial-index law has been obtained:For higher derivatives of these Pquations, their order and (algbraic) degrse have to satisfy a sim ple inequality. Especially, in the two dimensional space, a second order partial differential equation, which is a Euler-Lagrange equation, must be a Monge-Ampere equation.
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