387 citations · 936 across the 36 of their papers we have counts for
42 papers
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…
Schrödinger equation on Cartan-Hadamard manifolds with oscillating nonlinearities
Luigi Appolloni, Giovanni Molica Bisci, Simone Secchi
We study the equation on a -dimensional homogeneous Cartan-Hadamard Manifold with . Without using the theory of topological indices…
Multiple solutions for Schrödinger equations on Riemannian manifolds via -theorems
Luigi Appolloni, Giovanni Molica Bisci, Simone Secchi
We consider a smooth, complete and non-compact Riemannian manifold of dimension , and we look for positive solutions to the semilinear elliptic equation…
On Critical Kirchhoff problems driven by the fractional Laplacian
Luigi Appolloni, Giovanni Molica Bisci, Simone Secchi
We study a nonlocal parametric problem driven by the fractional Laplacian operator combined with a Kirchhoff-type coefficient and involving a critical nonlinearity term in the sens…
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…
Concentration phenomena for the Schrödinger-Poisson system in
Denis Bonheure, Silvia Cingolani, Simone Secchi
We perform a semiclassical analysis for the planar Schrödinger-Poisson system \[ \cases{ -\varepsilon^{2} Δψ+V(x)ψ= E(x) ψ\quad \text{in },\cr -ΔE= |ψ|^{2} \quad \tex…