23 citations · 232 across the 109 of their papers we have counts for
15 papers · 2 filters
Ground states for fractional Kirchhoff equations with critical nonlinearity in low dimension
Zhisu Liu, Marco Squassina, Jianjun Zhang
We study the existence of ground states to a nonlinear fractional Kirchhoff equation with an external potential . Under suitable assumptions on , using the monotonicity trick…
Singularly perturbed critical Choquard equations
Claudianor O. Alves, Fashun Gao, Marco Squassina +1
In this paper we study the semiclassical limit for the singularly perturbed Choquard equation $$ -\vr^2Δu +V(x)u =\vr^{μ-3}\Big(\int_{\R^3} \frac{Q(y)G(u(y))}{|x-y|^μ}dy\Big)Q(x)g(…
The Maz'ya-Shaposhnikova limit in the magnetic setting
Andrea Pinamonti, Marco Squassina, Eugenio Vecchi
We prove a magnetic version of the Maz'ya-Shaposhnikova singular limit of nonlocal norms with vanishing fractional parameter. This complements a general convergence result recently…
Recent progresses in the theory of nonlinear nonlocal problems
Sunra Mosconi, Marco Squassina
We overview some recent existence and regularity results in the theory of nonlocal nonlinear problems driven by the fractional -Laplacian.
Magnetic BV functions and the Bourgain-Brezis-Mironescu formula
Andrea Pinamonti, Marco Squassina, Eugenio Vecchi
We prove a general magnetic Bourgain-Brezis-Mironescu formula. In particular, after developing a theory of magnetic bounded variation functions, we prove the validity of the formul…
Existence results for double-phase problems via Morse theory
Kanishka Perera, Marco Squassina
We obtain nontrivial solutions for a class of double-phase problems using Morse theory. In the absence of a direct sum decomposition, we use a cohomological local splitting to get…