%0 Report %D 2021 %T On Dini derivatives of real functions %A Giuliano Klun %A Alessandro Fonda %A Andrea Sfecci %G eng %0 Journal Article %J Communications in Contemporary MathematicsCommunications in Contemporary Mathematics %D 2021 %T Non-well-ordered lower and upper solutions for semilinear systems of PDEs %A Alessandro Fonda %A Giuliano Klun %A Andrea Sfecci %X
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.
%B Communications in Contemporary MathematicsCommunications in Contemporary Mathematics %P 2150080 %8 2021/08/27 %@ 0219-1997 %G eng %U https://doi.org/10.1142/S0219199721500802 %! Commun. Contemp. Math. %0 Journal Article %D 2021 %T Periodic Solutions of Second-Order Differential Equations in Hilbert Spaces %A Alessandro Fonda %A Giuliano Klun %A Andrea Sfecci %XWe 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.
%V 18 %P 223 %8 2021/09/07 %@ 1660-5454 %G eng %U https://doi.org/10.1007/s00009-021-01857-8 %N 5 %! Mediterranean Journal of Mathematics %0 Journal Article %J Advanced Nonlinear Studies %D 2021 %T Well-Ordered and Non-Well-Ordered Lower and Upper Solutions for Periodic Planar Systems %A Alessandro Fonda %A Giuliano Klun %A Andrea Sfecci %B Advanced Nonlinear Studies %V 21 %P 397 - 419 %8 2021 %G eng %U https://doi.org/10.1515/ans-2021-2117 %N 2 %0 Journal Article %J Annali di Matematica Pura ed Applicata (1923 -) %D 2020 %T On functions having coincident p-norms %A Giuliano Klun %XIn 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: $\begin{aligned} \mu (\{x\in E:|f(x)|>\alpha \})=\mu (\{x\in E:|g(x)|>\alpha \})\quad \text { for all } \alpha \ge 0. \end{aligned}$
%B Annali di Matematica Pura ed Applicata (1923 -) %V 199 %P 955-968 %G eng %U https://doi.org/10.1007/s10231-019-00907-z %R 10.1007/s10231-019-00907-z %0 Journal Article %J NONLINEAR ANALYSIS %D 2020 %T Periodic solutions of nearly integrable Hamiltonian systems bifurcating from infinite-dimensional tori %A Alessandro Fonda %A Giuliano Klun %A Andrea Sfecci %XWe 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 TOPOLOGICAL METHODS IN NONLINEAR ANALYSIS %D 2019 %T On the topological degree of planar maps avoiding normal cones %A Alessandro Fonda %A Giuliano Klun %XThe 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 $1$.