7 papers · 1 filter
Mixed-dispersion Schrödinger equations and Gagliardo-Nirenberg inequalities: equivalence between ground states and optimizers
Zhisu Liu, Giulio Romani, Yu Su
We study a nonlinear Schrödinger equation with mixed dispersion in the mass competition regime, namely mass-supercritical for the Laplacian and mass-subcritical for the Bilaplacian…
A blow-up approach for a priori bounds in semilinear planar elliptic systems: the Brezis-Merle critical case
Laura Baldelli, Gabriele Mancini, Giulio Romani
We establish uniform a priori estimates for solutions of semilinear planar Hamiltonian elliptic systems in a ball with Dirichlet boundary conditions. We consider a broad class of c…
Positive solutions with prescribed mass for a planar Choquard equation with critical growth
Ling Huang, Giulio Romani
We study normalised solutions for a Choquard equation in the plane with polynomial Riesz kernel and exponential nonlinearities, which are critical in the sense of Trudinger-Moser.…
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…
Choquard equations with critical exponential nonlinearities in the zero mass case
Giulio Romani
We investigate Choquard equations in driven by a weighted -Laplace operator and with polynomial kernel and zero mass. Since the setting is limiting for the Sobolev…
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…