Euler-Lagrange equation

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This is a necessary condition for LaTeX: y to solve the classical problem in variational calculus:

LaTeX:  \mbox{div}(F_{\zeta} (x, y(x), \nabla y(x))) = F_{\lambda}(x, y(x), \nabla y(x)),

where LaTeX: F(x, \lambda, \zeta): 
\Omega \times \mathbb{R} \times \mathbb{R}^n \rightarrow \mathbb{R}.


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