Geodesic
The minimum existence of functional $\int_a^b F( x(t), y(t), \dot{x}(t), \dot{y}(t) ) dt$
Commentationes Mathematicae Universitatis Carolinae, Tome 11 (1970) no. 2, pp. 205-225

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Classification : 43Axx, 49-10 
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     author = {Sou\v{c}ek, Vladim{\'\i}r},
     title = {The minimum existence of functional $\int_a^b F( x(t), y(t), \dot{x}(t), \dot{y}(t) ) dt$},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     pages = {205--225},
     publisher = {mathdoc},
     volume = {11},
     number = {2},
     year = {1970},
     mrnumber = {0270246},
     zbl = {0197.41702},
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Souček, Vladimír. The minimum existence of functional $\int_a^b F( x(t), y(t), \dot{x}(t), \dot{y}(t) ) dt$. Commentationes Mathematicae Universitatis Carolinae, Tome 11 (1970) no. 2, pp. 205-225. http://geodesic.mathdoc.fr/item/CMUC_1970__11_2_a1/