Geodesic
Periodic Solutions For ẋ = Ax + G(x, t) + ∊p(t)
Canadian mathematical bulletin, Tome 14 (1971) no. 4, pp. 575-577

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

We wish to establish the existence of a periodic solution to 1 where x, g and p are n-vectors, A is an n × n constant matrix, and ∊ is a small scalar parameter. We assume that g and p are locally Lipschitz in x and continuous and T-periodic in t, and that the origin is a point of asymptotically stable equilibrium, when ∊ = 0. 
Ponzo, Peter J. Periodic Solutions For ẋ = Ax + G(x, t) + ∊p(t). Canadian mathematical bulletin, Tome 14 (1971) no. 4, pp. 575-577. doi: 10.4153/CMB-1971-105-4
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[1] 1. Cesari, L., Asymptotic behaviour and stability problems in ordinary differential equations, Springer-Verlag, Berlin (1963), 115-182. Google Scholar

[2] 2. Freedman, H. I., Estimates on the existence region for periodic solutions of equations involving a small parameter, SIAM J. Appl. Math. 16 (1968), 1341-1349. Google Scholar

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