@article {2021, title = {Periodic Solutions of Second-Order Differential Equations in Hilbert Spaces}, volume = {18}, year = {2021}, month = {2021/09/07}, pages = {223}, abstract = {

We prove the existence of periodic solutions of some infinite-dimensional systems by the use of the lower/upper solutions method. Both the well-ordered and non-well-ordered cases are treated, thus generalizing to systems some well-established results for scalar equations.

}, isbn = {1660-5454}, url = {https://doi.org/10.1007/s00009-021-01857-8}, author = {Alessandro Fonda and Giuliano Klun and Andrea Sfecci} } @article {2020, title = {Periodic solutions of nearly integrable Hamiltonian systems bifurcating from infinite-dimensional tori}, journal = {NONLINEAR ANALYSIS}, year = {2020}, abstract = {

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 Poincar{\'e}{\textendash}Birkhoff Theorem.

}, issn = {0362-546X}, doi = {10.1016/j.na.2019.111720}, url = {https://doi.org/10.1016/j.na.2019.111720}, author = {Alessandro Fonda and Giuliano Klun and Andrea Sfecci} } @article {fonda2016periodic, title = {Periodic perturbations of Hamiltonian systems}, journal = {Advances in Nonlinear Analysis}, volume = {5}, number = {4}, year = {2016}, pages = {367{\textendash}382}, publisher = {De Gruyter}, abstract = {

We prove existence and multiplicity results for periodic solutions of Hamiltonian systems, by the use of a higher dimensional version of the Poincar{\'e}{\textendash}Birkhoff fixed point theorem. The first part of the paper deals with periodic perturbations of a completely integrable system, while in the second part we focus on some suitable global conditions, so to deal with weakly coupled systems.

}, doi = {10.1515/anona-2015-0122}, author = {Alessandro Fonda and Maurizio Garrione and Paolo Gidoni} } @article {FONDA201573, title = {A permanence theorem for local dynamical systems}, journal = {Nonlinear Analysis: Theory, Methods \& Applications}, volume = {121}, year = {2015}, note = {Nonlinear Partial Differential Equations, in honor of Enzo Mitidieri for his 60th birthday}, pages = {73 - 81}, abstract = {

We provide a necessary and sufficient condition for permanence related to a local dynamical system on a suitable topological space. We then present an illustrative application to a Lotka{\textendash}Volterra predator{\textendash}prey model with intraspecific competition.

}, keywords = {Lotka{\textendash}Volterra, permanence, Predator{\textendash}prey, Uniform persistence}, issn = {0362-546X}, doi = {https://doi.org/10.1016/j.na.2014.10.011}, url = {http://www.sciencedirect.com/science/article/pii/S0362546X14003332}, author = {Alessandro Fonda and Paolo Gidoni} } @article {fonda2013periodic, title = {Periodic bouncing solutions for nonlinear impact oscillators}, journal = {Advanced Nonlinear Studies}, volume = {13}, number = {1}, year = {2013}, pages = {179{\textendash}189}, publisher = {Advanced Nonlinear Studies, Inc.}, doi = {10.1515/ans-2013-0110}, author = {Alessandro Fonda and Andrea Sfecci} } @article {fonda2012, title = {Periodic solutions of a system of coupled oscillators with one-sided superlinear retraction forces}, journal = {Differential Integral Equations}, volume = {25}, number = {11/12}, year = {2012}, month = {11}, pages = {993{\textendash}1010}, publisher = {Khayyam Publishing, Inc.}, url = {https://projecteuclid.org:443/euclid.die/1356012248}, author = {Alessandro Fonda and Andrea Sfecci} }