In this paper we study the ordinary differential equation x'' + q(t)g(x) = 0, where g is a locally Lipschitz continuous function that satisfies g(x)x > 0 for all non zero x and is asymptotically linear, while q is a continuous, π-periodic and changing sign weight. By the application of a recent result on the existence and multiplicity of fixed points of planar maps, we give conditions on q and on the behavior of the ratio g(x)/x near zero and near infinity in order to obtain multiple periodic solutions with the prescribed number of zeros in the intervals of positivity and negativity of q, as well as multiple subharmonics of any order and uncountably many bounded solutions.

Dambrosio, W., & Papini, D. (2004). Periodic solutions of asymptotically linear second order equations with changing sign weight. ANNALI DI MATEMATICA PURA ED APPLICATA, 183(4), 537-554 [10.1007/s10231-004-0104-x].

Periodic solutions of asymptotically linear second order equations with changing sign weight

PAPINI, DUCCIO
2004

Abstract

In this paper we study the ordinary differential equation x'' + q(t)g(x) = 0, where g is a locally Lipschitz continuous function that satisfies g(x)x > 0 for all non zero x and is asymptotically linear, while q is a continuous, π-periodic and changing sign weight. By the application of a recent result on the existence and multiplicity of fixed points of planar maps, we give conditions on q and on the behavior of the ratio g(x)/x near zero and near infinity in order to obtain multiple periodic solutions with the prescribed number of zeros in the intervals of positivity and negativity of q, as well as multiple subharmonics of any order and uncountably many bounded solutions.
Dambrosio, W., & Papini, D. (2004). Periodic solutions of asymptotically linear second order equations with changing sign weight. ANNALI DI MATEMATICA PURA ED APPLICATA, 183(4), 537-554 [10.1007/s10231-004-0104-x].
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11365/23160
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