In a measure space $(X,{\mathcal {A}},\mu )$, we consider two measurable functions $f,g:E\rightarrow {\mathbb {R}}$, for some $E\in {\mathcal {A}}$. We prove that the property of having equal p-norms when p varies in some infinite set $P\subseteq [1,+\infty )$ is equivalent to the following condition: $\begin{aligned} \mu (\{x\in E:|f(x)|\>\alpha \})=\mu (\{x\in E:|g(x)|\>\alpha \})\quad \text { for all } \alpha \ge 0. \end{aligned}$

}, doi = {10.1007/s10231-019-00907-z}, url = {https://doi.org/10.1007/s10231-019-00907-z}, author = {Giuliano Klun} } @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 {2019, title = {On the topological degree of planar maps avoiding normal cones}, journal = {TOPOLOGICAL METHODS IN NONLINEAR ANALYSIS}, volume = {53}, number = {SISSA;04/2019/MATE}, year = {2019}, pages = {825-845}, publisher = {SISSA}, abstract = {The classical Poincar{\'e}-Bohl theorem provides the existence of a zero for a function avoiding external rays. When the domain is convex, the same holds true when avoiding normal cones.

We consider here the possibility of dealing with nonconvex sets having inward corners or cusps, in which cases the normal cone vanishes. This allows us to deal with situations where the topological degree may be strictly greater than $1$.