We prove the existence of periodic solutions of some infinite-dimensional nearly integrable Hamiltonian systems, bifurcating from infinite-dimensional tori, by the use of a generalization of the Poincaré–Birkhoff Theorem.

%B NONLINEAR ANALYSIS %G eng %U https://doi.org/10.1016/j.na.2019.111720 %R 10.1016/j.na.2019.111720 %0 Journal Article %J Advanced Nonlinear Studies %D 2013 %T Periodic bouncing solutions for nonlinear impact oscillators %A Alessandro Fonda %A Andrea Sfecci %B Advanced Nonlinear Studies %I Advanced Nonlinear Studies, Inc. %V 13 %P 179–189 %G eng %R 10.1515/ans-2013-0110 %0 Journal Article %J Journal of Differential Equations %D 2012 %T A general method for the existence of periodic solutions of differential systems in the plane %A Alessandro Fonda %A Andrea Sfecci %K Nonlinear dynamics %K Periodic solutions %XWe propose a general method to prove the existence of periodic solutions for planar systems of ordinary differential equations, which can be used in many different circumstances. Applications are given to some nonresonant cases, even for systems with superlinear growth in some direction, or with a singularity. Systems “at resonance” are also considered, provided a Landesman–Lazer type of condition is assumed.

%B Journal of Differential Equations %V 252 %P 1369 - 1391 %G eng %U http://www.sciencedirect.com/science/article/pii/S0022039611003196 %R https://doi.org/10.1016/j.jde.2011.08.005 %0 Journal Article %J Nonlinear Analysis: Theory, Methods & Applications %D 2012 %T A nonresonance condition for radial solutions of a nonlinear Neumann elliptic problem %A Andrea Sfecci %K Neumann problem %K Nonresonance %K Radial solutions %K Time-map %XWe prove an existence result for radial solutions of a Neumann elliptic problem whose nonlinearity asymptotically lies between the first two eigenvalues. To this aim, we introduce an alternative nonresonance condition with respect to the second eigenvalue which, in the scalar case, generalizes the classical one, in the spirit of Fonda et al. (1991) [2]. Our approach also applies for nonlinearities which do not necessarily satisfy a subcritical growth assumption.

%B Nonlinear Analysis: Theory, Methods & Applications %V 75 %P 6191 - 6202 %G eng %U http://www.sciencedirect.com/science/article/pii/S0362546X12002659 %R https://doi.org/10.1016/j.na.2012.06.023 %0 Journal Article %J Differential Integral Equations %D 2012 %T Periodic solutions of a system of coupled oscillators with one-sided superlinear retraction forces %A Alessandro Fonda %A Andrea Sfecci %B Differential Integral Equations %I Khayyam Publishing, Inc. %V 25 %P 993–1010 %8 11 %G eng %U https://projecteuclid.org:443/euclid.die/1356012248