Given a smooth function U(t, x), T-periodic in the first variable and satisfying U(t, x) = O(vertical bar x vertical bar(alpha)) for some alpha is an element of (0, 2) as vertical bar x vertical bar -> infinity, we prove that the forced Kepler problem(sic) = -x/vertical bar x vertical bar(3) + del U-x(t, x), x is an element of R-2,has a generalized T-periodic solution, according to the definition given in the paper by A. Boscaggin, R. Ortega, and L. Zhao [Trans. Amer. Math. Soc. 372 (2019), 677-703]. The proof relies on variational arguments.
Periodic solutions to a forced kepler problem in the plane / Boscaggin, A.; Dambrosio, W.; Papini, D.. - In: PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY. - ISSN 0002-9939. - 148:1(2020), pp. 301-314. [10.1090/proc/14719]
Periodic solutions to a forced kepler problem in the plane
Papini D.
2020
Abstract
Given a smooth function U(t, x), T-periodic in the first variable and satisfying U(t, x) = O(vertical bar x vertical bar(alpha)) for some alpha is an element of (0, 2) as vertical bar x vertical bar -> infinity, we prove that the forced Kepler problem(sic) = -x/vertical bar x vertical bar(3) + del U-x(t, x), x is an element of R-2,has a generalized T-periodic solution, according to the definition given in the paper by A. Boscaggin, R. Ortega, and L. Zhao [Trans. Amer. Math. Soc. 372 (2019), 677-703]. The proof relies on variational arguments.
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