Geodesic
On the Cauchy problem for the differential equation f(t, x, x′, ..., x(k)) = 0
Glasgow mathematical journal, Tome 33 (1991) no. 3, pp. 343-348

Voir la notice de l'article provenant de la source Cambridge University Press

In the sequel, given k, n ∈ N, p ∈ [1, ∞] and a compact real interval I, we denote by Wk, p(I, Rn) (simply by Wk,p(I if n = 1) the space of all functions u ∈ Ck−1(I, Rn) such that uk−1 is absolutely continuous in I and u(k) ∈ Lp (I, Rn).Very recently, in [11], J. R. L. Webb and S. C. Welsh obtained the following existence result. 
Ricceri, Biagio. On the Cauchy problem for the differential equation f(t, x, x′, ..., x(k)) = 0. Glasgow mathematical journal, Tome 33 (1991) no. 3, pp. 343-348. doi: 10.1017/S0017089500008405
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