5 citations · 9 across the 9 of their papers we have counts for
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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 suit…
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…
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…
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…
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 em…
Compact embeddings for weighted fractional Sobolev spaces and applications to Nonlinear Schrödinger Equations
Federico Bernini, Sergio Rolando, Simone Secchi
The aim of this work is to prove a compact embedding for a weighted fractional Sobolev spaces. As an application, we use this embedding to prove, via variational methods, the exist…
Generalized linking-type theorem with applications to strongly indefinite problems with sign-changing nonlinearities
Federico Bernini, Bartosz Bieganowski
We show the linking-type result which allows us to study strongly indefinite problems with sign-changing nonlinearities. We apply the abstract theory to the singular Schrödinger eq…
Semirelativistic Choquard equations with singular potentials and general nonlinearities arising from Hartree-Fock theory
Federico Bernini, Bartosz Bieganowski, Simone Secchi
We are interested in the general Choquard equation \begin{multline*} \sqrt{\strut -Δ+ m^2} \ u - mu + V(x)u - \fracμ{|x|} u = \left( \int_{\mathbb{R}^N} \frac{F(y,u(y))}{|x-y|^{N-α…