Geodesic
Periodic solutions of the Hamilton–Jacobi equation with a periodic non-homogeneous term and Aubry–Mather theory
Sbornik. Mathematics, Tome 190 (1999) no. 10, pp. 1487-1504 Cet article a éte moissonné depuis la source Math-Net.Ru

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It is proved that the one-dimensional Hamilton–Jacobi equation with a periodic non-homogeneous term admits a family of generalized solutions, each of which can be represented as the sum of a linear and a periodic function; a condition for the uniqueness of such a solution is given in terms of Aubry–Mather theory. 
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     title = {Periodic solutions of the {Hamilton{\textendash}Jacobi} equation with a~periodic non-homogeneous term and {Aubry{\textendash}Mather} theory},
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A. N. Sobolevskii. Periodic solutions of the Hamilton–Jacobi equation with a periodic non-homogeneous term and Aubry–Mather theory. Sbornik. Mathematics, Tome 190 (1999) no. 10, pp. 1487-1504. http://geodesic.mathdoc.fr/item/SM_1999_190_10_a4/

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