6 papers
Existence and regularity for an entire Grushin-Choquard equation
Federico Bernini, Paolo Malanchini
We consider the following Choquard equation where is the Grushin operator. For a…
Qualitative properties of the fractional magnetic -Laplacian and applications to critical quasilinear problems
Laura Baldelli, Federico Bernini
We investigate the fractional magnetic -Laplacian operator in the physical dimension case , with and . Our goal is twofold. First, we define and study suita…
Nonlinear Schrödinger-Poisson systems in dimension two: the zero mass case
Federico Bernini, Giulio Romani, Cristina Tarsi
We provide an existence result for a Schrödinger-Poisson system in gradient form, set in the whole plane, in the case of zero mass. Since the setting is limiting for the Sobolev e…
Multiplicity of critical orbits to nonlinear, strongly indefinite functionals with sign-changing nonlinear part
Federico Bernini, Bartosz Bieganowski, Daniel Strzelecki
We show an abstract critical point theorem about existence of infinitely many critical orbits to strongly indefinite functionals with sign-changing nonlinear part defined on a disl…
Note on homoclinic solutions to nonautonomous Hamiltonian systems with sign-changing nonlinear part
Federico Bernini, Bartosz Bieganowski, Daniel Strzelecki
In the paper, we utilize the recent variational, abstract theorem to show the existence of homoclinic solutions to the Hamiltonian system $$ \dot{z} = J D_z H(z, t), \quad t \in \m…
On a fractional magnetic pseudorelativistic operator: properties and applications
Federico Bernini, Pietro d'Avenia
We introduce a fractional magnetic pseudorelativistic operator for a general fractional order . First we define a suitable functional setting and we prove some fundament…