58 citations · 102 across the 23 of their papers we have counts for
25 papers
Normalised Hamiltonian Elliptic Systems: a Gagliardo-Nirenberg inequality for bilinear mass
Daniele Cassani, Giulio Romani
We study Hamiltonian elliptic systems with prescribed bilinear mass . We establish a Gagliardo--Nirenberg inequality in the crossed gradient pairing and…
Positive radial ground states for nonlinear biharmonic equations: maximum principles and expanding-domain approximation
Daniele Cassani, Zhisu Liu, Giulio Romani +1
We prove the existence of nonnegative radial ground states for a class of nonlinear biharmonic equations in , covering subcritical and critical nonlinearities. The sol…
The mass-mixed case for normalized solutions to NLS equations in dimension two
Daniele Cassani, Ling Huang, Cristina Tarsi +1
\noindent We are concerned with positive normalized solutions to the following semi-linear Schrödinger equations $$ -Δu+λu=f(u), \quad\…
Existence of infinitely many solutions for a critical Hartree type equation with potential: local Pohožaev identities methods
Daniele Cassani, Minbo Yang, Xinyun Zhang
This paper deals with the following equation $$-Δu =K(|x'|, x'')\Big(|x|^{-α}\ast (K(|x'|, x'')|u|^{2^{\ast}_α})\Big) |u|^{2^{\ast}_α-2}u\quad\mbox{in}\ \mathbb{R}^N,$$ where $N\ge…
Nonlocal Schrödinger-Poisson systems in : the fractional Sobolev limiting case
Daniele Cassani, Zhisu Liu, Giulio Romani
We study the existence of positive solutions for nonlocal systems in gradient form and set in the whole . A quasilinear fractional Schrödinger equation, where the lead…
Global vs blow-up solutions and optimal threshold for hyperbolic ODEs with possibly singular nonlinearities
Daniele Cassani, Tosiya Miyasita
We consider a hyperbolic ordinary differential equation perturbed by a nonlinearity which can be singular at a point and in particular this includes MEMS type equations. We first s…