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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…
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}+\…
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…