16 papers · 1 filter
Continuation theorems for periodic systems and applications to problems with nonlinear time-dependent differential operators
Pierluigi Benevieri, Guglielmo Feltrin
In this paper we propose some continuation theorems for the periodic problem \begin{equation*} \begin{cases} \, x_{i}' = g_{i}(t,x_{i+1}), &i=1,\ldots,n-1, \\ \, x_{n}' = h(t,x_{1}…
A Poincaré-Birkhoff theorem for multivalued successor maps with applications to periodic superlinear Hamiltonian systems
Guglielmo Feltrin, Alessandro Fonda, Andrea Sfecci
We provide a new version of the Poincaré-Birkhoff theorem for possibly multivalued successor maps associated with planar non-autonomous Hamiltonian systems. As an application, we p…
Atypical bifurcation for periodic solutions of -Laplacian systems
Pierluigi Benevieri, Guglielmo Feltrin
In this paper, we study the -periodic solutions of the parameter-dependent -Laplacian equation \begin{equation*} (ϕ(x'))'=F(λ,t,x,x'). \end{equation*} Based on the topologica…
Periodic solutions to superlinear indefinite planar systems: a topological degree approach
Guglielmo Feltrin, Juan Carlos Sampedro, Fabio Zanolin
We deal with a planar differential system of the form \begin{equation*} \begin{cases} \, u' = h(t,v), \\ \, v' = - λa(t) g(u), \end{cases} \end{equation*} where is -periodic…
Equilibrium points, periodic solutions and the Brouwer fixed point theorem for convex and non-convex domains
Guglielmo Feltrin, Fabio Zanolin
We show the direct applicability of the Brouwer fixed point theorem for the existence of equilibrium points and periodic solutions for differential systems on general domains satis…
Uniqueness of positive solutions for boundary value problems associated with indefinite -Laplacian type equations
Alberto Boscaggin, Guglielmo Feltrin, Fabio Zanolin
The paper provides a uniqueness result for positive solutions of the Neumann and periodic boundary value problems associated with the -Laplacian equation \begin{equation*} \bigl…