Abstract.
We study a second order scalar equation of the form x′′ + V′(x) = p(t), where p is a π-perodic function and V is a singular potential. We give sufficient conditions on V, p ensuring that all solutions are bounded; we prove the existence of Aubry–Mather sets as well.
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Under the auspices of GNAMPA-I.N.d.A.M., Italy and NNSF of China. The work has been performed in the frame of the M.I.U.R. Project ’Metodi Variazionali e Topologici nello Studio di Fenomeni Non Lineari’ and by the GNAMPA-I.N.d.A.M. Project ’Equazioni Differenziali Ordinarie Non Lineari: Teoria ed Applicazioni’ and NNSF of China 10325103.
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Capietto, A., Dambrosio, W. & Liu, B. On the boundedness of solutions to a nonlinear singular oscillator. Z. Angew. Math. Phys. 60, 1007 (2009). https://doi.org/10.1007/s00033-008-8094-y
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DOI: https://doi.org/10.1007/s00033-008-8094-y