Year: 2017
Type: preprint
Abstract: We discuss the existence of ground state solutions for the Choquard equation $$-Δu=(I_α*F(u))F'(u)\quad\quad\quad\text{in }\mathbb R^N.$$ We prove the existence of solutions under general hypotheses, investigating in particular the case of a homogeneous nonlinearity $F(u)=\frac{|u|^p}p$. The cases $N=2$ and $N\ge3$ are treated differently in some steps. The solutions are found through a variational mountain pass strategy. The result presented are contained in the papers with arXiv ID 1212.2027 and 1604.03294
Source: arXiv (Cornell University)
Author: Battaglia, Luca
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2579005708