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.

UR - https://doi.org/10.1016/j.na.2019.111720 ER - TY - JOUR T1 - Periodic bouncing solutions for nonlinear impact oscillators JF - Advanced Nonlinear Studies Y1 - 2013 A1 - Alessandro Fonda A1 - Andrea Sfecci PB - Advanced Nonlinear Studies, Inc. VL - 13 ER - TY - JOUR T1 - A general method for the existence of periodic solutions of differential systems in the plane JF - Journal of Differential Equations Y1 - 2012 A1 - Alessandro Fonda A1 - Andrea Sfecci KW - Nonlinear dynamics KW - Periodic solutions AB -We 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.

VL - 252 UR - http://www.sciencedirect.com/science/article/pii/S0022039611003196 ER - TY - JOUR T1 - A nonresonance condition for radial solutions of a nonlinear Neumann elliptic problem JF - Nonlinear Analysis: Theory, Methods & Applications Y1 - 2012 A1 - Andrea Sfecci KW - Neumann problem KW - Nonresonance KW - Radial solutions KW - Time-map AB -We 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.

VL - 75 UR - http://www.sciencedirect.com/science/article/pii/S0362546X12002659 ER - TY - JOUR T1 - Periodic solutions of a system of coupled oscillators with one-sided superlinear retraction forces JF - Differential Integral Equations Y1 - 2012 A1 - Alessandro Fonda A1 - Andrea Sfecci PB - Khayyam Publishing, Inc. VL - 25 UR - https://projecteuclid.org:443/euclid.die/1356012248 ER -