Geodesic
Field-theory models that admit alternative Lagrangian formulations. I
Teoretičeskaâ i matematičeskaâ fizika, Tome 89 (1991) no. 1, pp. 121-131 
F. A. Lunev. Field-theory models that admit alternative Lagrangian formulations. I. Teoretičeskaâ i matematičeskaâ fizika, Tome 89 (1991) no. 1, pp. 121-131. http://geodesic.mathdoc.fr/item/TMF_1991_89_1_a10/
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Some theorems are proved concerning the structure of Lagrangian systems of differential equations for which the Lagrangian is not uniquely determined. In particular, a complete description is obtained for bi-Lagrangian systems of second order with hyperregular Lagrangians quadratic in the derivatives.

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