11 citations · 48 across the 18 of their papers we have counts for
20 papers
Reparametrizing the relativistic Kepler equation: a bridge to Levi-Civita-type models
Alberto Boscaggin, Walter Dambrosio
We establish a link between different relativistic variants of the Kepler problem. In particular, we show that solutions of the special relativistic model with fixed energy can be…
Bifurcation of closed orbits of Hamiltonian systems with application to geodesics of the Schwarzschild metric
Alberto Boscaggin, Walter Dambrosio, Guglielmo Feltrin
We investigate bifurcation of closed orbits with a fixed energy level for a class of nearly integrable Hamiltonian systems with two degrees of freedom. More precisely, we make a jo…
Prescribed energy periodic solutions of Kepler problems with relativistic corrections
Alberto Boscaggin, Walter Dambrosio, Guglielmo Feltrin
We consider two different relativistic versions of the Kepler problem in the plane: the first one involves the relativistic differential operator, the second one involves a correct…
Infinitely many periodic solutions to a Lorentz force equation with singular electromagnetic potential
Alberto Boscaggin, Walter Dambrosio, Duccio Papini
We consider the Lorentz force equation $$ \frac{d}{dt}\left(\frac{m\dot{x}}{\sqrt{1-|\dot{x}|^{2}/c^{2}}}\right) = q \left(E(t,x) + \dot x \times B(t,x)\right), \qquad x \in \mathb…
A Maupertuis-type principle in relativistic mechanics and applications
Alberto Boscaggin, Walter Dambrosio, Eduardo Muñoz-Hernández
We provide a Maupertuis-type principle for the following system of ODE, of interest in special relativity: $$ \frac{\rm d}{{\rm d}t}\left(\frac{m\dot{x}}{\sqrt{1-|\dot{x}|^2/c^2}}\…
Periodic solutions to relativistic Kepler problems: a variational approach
Alberto Boscaggin, Walter Dambrosio, Duccio Papini
We study relativistic Kepler problems in the plane. At first, using non-smooth critical point theory, we show that under a general time-periodic external force of gradient type the…
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…
Unbounded solutions to a system of coupled asymmetric oscillators at resonance
Alberto Boscaggin, Walter Dambrosio, Duccio Papini
We deal with the following system of coupled asymmetric oscillators \[ \begin{cases} \ddot{x}_1+a_1x_1^+-b_1x^-_1+ϕ_1(x_2)=p_1(t) \\ \ddot{x}_2+a_2\,x_2^+-b_2\,x^-_2+ϕ_2(x_1)=p_2(t…
Unbounded solutions to systems of differential equations at resonance
Alberto Boscaggin, Walter Dambrosio, Duccio Papini
We deal with a weakly coupled system of ODEs of the type with locally Lipschitz continuous and…
Periodic solutions to a perturbed relativistic Kepler problem
Alberto Boscaggin, Walter Dambrosio, Guglielmo Feltrin
We consider a perturbed relativistic Kepler problem \begin{equation*} \dfrac{\mathrm{d}}{\mathrm{d}t}\left(\dfrac{m\dot{x}}{\sqrt{1-|\dot{x}|^2/c^2}}\right)=-α\, \dfrac{x}{|x|^3}+\…
On the minimality of Keplerian arcs with fixed negative energy
Vivina Barutello, Alberto Boscaggin, Walter Dambrosio
We revisit a classical result by Jacobi on the local minimality, as critical points of the corresponding energy functional, of fixed-energy solutions of the Kepler equation joining…
Parabolic orbits in Celestial Mechanics: a functional-analytic approach
Alberto Boscaggin, Walter Dambrosio, Guglielmo Feltrin +1
We prove the existence of half-entire parabolic solutions, asymptotic to a prescribed central configuration, for the equation \begin{equation*} \ddot{x} = \nabla U(x) + \nabla W(t,…
Periodic solutions to a forced Kepler problem in the plane
A. Boscaggin, W. Dambrosio, D. Papini
Given a smooth function , -periodic in the first variable and satisfying for some as , we…
The spatial -centre problem: scattering at positive energies
A. Boscaggin, A. Bottois, W. Dambrosio
For the spatial generalized -centre problem $$ \ddot{x} = -\sum_{i=1}^{N} \frac{m_i (x - c_i)}{\vert x - c_i \vert^{α+2}},\qquad x \in \mathbb{R}^3 \setminus \{c_1,\dots,c_N \},…
Parabolic solutions for the planar -centre problem: multiplicity and scattering
Alberto Boscaggin, Walter Dambrosio, Duccio Papini
For the planar -centre problem where for…
Multiple positive solutions to elliptic boundary blow-up problems
Alberto Boscaggin, Walter Dambrosio, Duccio Papini
We prove the existence of multiple positive radial solutions to the sign-indefinite elliptic boundary blow-up problem \[ \left\{\begin{array}{ll} Δu + \bigl(a^+(\vert x \vert) - μa…
Scattering parabolic solutions for the spatial N-centre problem
Alberto Boscaggin, Walter Dambrosio, Susanna Terracini
For the -centre problem in the three dimensional space, $$ \ddot x = -\sum_{i=1}^{N} \frac{m_i \,(x-c_i)}{\vert x - c_i \vert^{α+2}}, \qquad x \in \mathbb{R}^3 \setminus \{c_1,\…
Asymptotic and chaotic solutions of a singularly perturbed Nagumo-type equation
Alberto Boscaggin, Walter Dambrosio, Duccio Papini
We deal with the singularly perturbed Nagumo-type equation where is a real parameter and is a piecewise co…
Highly oscillatory solutions of a Neumann problem for a -laplacian equation
Alberto Boscaggin, Walter Dambrosio
We deal with a boundary value problem of the form where for and , and $W:[…
Linear and nonlinear eigenvalue problems for Dirac systems in unbounded domains
Anna Capietto, Walter Dambrosio, Duccio Papini
We first study the linear eigenvalue problem for a planar Dirac system in the open half-line and describe the nodal properties of its solution by means of the rotation number. We t…