19 papers
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…
Periodic perturbations of central force problems and an application to a restricted -body problem
Alberto Boscaggin, Walter Dambrosio, Guglielmo Feltrin
We consider a perturbation of a central force problem of the form \begin{equation*} \ddot x = V'(|x|) \frac{x}{|x|} + \varepsilon \,\nabla_x U(t,x), \quad x \in \mathbb{R}^{2} \set…
On the number of positive solutions to an indefinite parameter-dependent Neumann problem
Guglielmo Feltrin, Elisa Sovrano, Andrea Tellini
We study the second-order boundary value problem \begin{equation*} \begin{cases} \, -u''=a_{λ,μ}(t) \, u^{2}(1-u), & t\in(0,1), \\ \, u'(0)=0, \quad u'(1)=0, \end{cases} \end{equat…
Bound sets for a class of -Laplacian operators
Guglielmo Feltrin, Fabio Zanolin
We provide an extension of the Hartman-Knobloch theorem for periodic solutions of vector differential systems to a general class of -Laplacian differential operators. Our main t…
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…