4 papers
Ground states of a nonlocal variational problem and Thomas-Fermi limit for the Choquard equation
Damiano Greco, Yanghong Huang, Zeng Liu +1
We study nonnegative optimizers of a Gagliardo-Nirenberg type inequality $$\iint_{\mathbb{R}^N \times \mathbb{R}^N} \frac{|u(x)|^p\,|u(y)|^p}{|x - y|^{N-α}} dx\, dy\le C\Big(\int_…
Thomas-Fermi theory of out-of-plane charge screening in graphene
Vitaly Moroz, Cyrill B. Muratov
This paper provides a variational treatment of the effect of external charges on the free charges in an infinite free-standing graphene sheet within the Thomas-Fermi theory. We est…
On the Phragmén-Lindelöf and the superposition principles for the -Laplacian
Pier Domenico Lamberti, Vitaly Moroz
We study sub and supersolutions for the -Laplace type elliptic equation of the form where is a radially symmetric domain in ${…
Asymptotic profiles of ground state solutions for Choquard equations with a general local perturbation
Shiwang Ma, Vitaly Moroz
In this paper, we study the asymptotic behavior of ground state solutions for the nonlinear Choquard equation with a general local perturbation $$ -Îu+\varepsilon u=(I_α\ast |u|^…