We prove existence results for systems of boundary value problems involving elliptic second-order differential operators. The assumptions involve lower and upper solutions, which may be either well-ordered, or not at all. The results are stated in an abstract framework, and can be translated also for systems of parabolic type.We prove existence results for systems of boundary value problems involving elliptic second-order differential operators. The assumptions involve lower and upper solutions, which may be either well-ordered, or not at all. The results are stated in an abstract framework, and can be translated also for systems of parabolic type.

SN - 0219-1997 UR - https://doi.org/10.1142/S0219199721500802 JO - Commun. Contemp. Math. ER - TY - JOUR T1 - Periodic Solutions of Second-Order Differential Equations in Hilbert Spaces Y1 - 2021 A1 - Alessandro Fonda A1 - Giuliano Klun A1 - Andrea Sfecci AB -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.

VL - 18 SN - 1660-5454 UR - https://doi.org/10.1007/s00009-021-01857-8 IS - 5 JO - Mediterranean Journal of Mathematics ER - TY - JOUR T1 - Well-Ordered and Non-Well-Ordered Lower and Upper Solutions for Periodic Planar Systems JF - Advanced Nonlinear Studies Y1 - 2021 A1 - Alessandro Fonda A1 - Giuliano Klun A1 - Andrea Sfecci VL - 21 UR - https://doi.org/10.1515/ans-2021-2117 IS - 2 ER - TY - JOUR T1 - On functions having coincident p-norms JF - Annali di Matematica Pura ed Applicata (1923 -) Y1 - 2020 A1 - Giuliano Klun AB -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: $\begin{aligned} \mu (\{x\in E:|f(x)|>\alpha \})=\mu (\{x\in E:|g(x)|>\alpha \})\quad \text { for all } \alpha \ge 0. \end{aligned}$

VL - 199 UR - https://doi.org/10.1007/s10231-019-00907-z ER - TY - JOUR T1 - Periodic solutions of nearly integrable Hamiltonian systems bifurcating from infinite-dimensional tori JF - NONLINEAR ANALYSIS Y1 - 2020 A1 - Alessandro Fonda A1 - Giuliano Klun A1 - Andrea Sfecci AB -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 - On the topological degree of planar maps avoiding normal cones JF - TOPOLOGICAL METHODS IN NONLINEAR ANALYSIS Y1 - 2019 A1 - Alessandro Fonda A1 - Giuliano Klun AB -The classical Poincaré-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 $1$.