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.
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

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[2] H. Hochstadt: Differential Equations, A Modern Approach. Holt, Rinehart and Winston, New York, Chicago, San Francisco, Toronto, London, 1964. | MR | Zbl

[3] A. Kufner J. Kadlec: Fourier Series. Academia, Prague, 1971. | MR

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