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math.AP2024
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 $$\iint_{\mathbb{R}^N \times \mathbb{R}^N} \frac{|u(x)|^p\,|u(y)|^p}{|x - y|^{N-α}} dx\, dy\le C\Big(\int_{…
math.AP2024
On the Phragmén-Lindelöf and the superposition principles for the -Laplacian
Pier Domenico Lamberti, Vitaly Moroz
We study sub and supersolutions for the -Laplace type elliptic equation of the form where is a radially symmetric domain in ${\ma…
math.AP2024
Asymptotic profiles of ground state solutions for Choquard equations with a general local perturbation
Shiwang Ma, Vitaly Moroz
In this paper, we study the asymptotic behavior of ground state solutions for the nonlinear Choquard equation with a general local perturbation $$ -Δu+\varepsilon u=(I_α\ast |u|^{p…