Geodesic
On non-existence of periodic solutions of an important differential equation
Applications of Mathematics, Tome 18 (1973) no. 4, pp. 213-226.

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The equations of variation with respect to the straight-lineequilibrium points $L_1,L_2,L_3$ of the elliptic three-dimensional restricted problem of three bodies are equivalent to a system of two differential equations of the second order and one Hill's equation. In the paper presented here, this Hill's equation is studied and a proof is given that this differential equation has no nontrivial periodic solution.
DOI : 10.21136/AM.1973.103474
Classification : 34B30, 34C25, 70F10 
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Matas, Vladimír. On non-existence of periodic solutions of an important differential equation. Applications of Mathematics, Tome 18 (1973) no. 4, pp. 213-226. doi : 10.21136/AM.1973.103474. http://geodesic.mathdoc.fr/articles/10.21136/AM.1973.103474/

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