Geodesic
Existence and nonexistence of nontrivial solutions for Choquard type equations
Electronic Journal of Differential Equations, Tome 2016 (2016).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: In this article, we consider the nonlocal problem $$ -\Delta u+u=q(x)\Big(\int_{\mathbb{R}^N}\frac{q(y)|u(y)|^p}{|x-y|^{N-\alpha}}dy \Big)|u|^{p-2}u,\quad x\in \mathbb{R}^N, $$ where $N\geq 3, \alpha\in (0,N), \frac{N+\alpha}{N}$ and $q(x)$ is a given potential. Under suitable assumptions on $q(x)$, we prove the existence and nonexistence of nontrivial solutions.
Classification : 35A15, 35J20, 35J60
Keywords: Choquard equation, nonlocal nonlinearities, variational methods 
@article{EJDE_2016__2016__a20,
     author = {Wang, Tao},
     title = {Existence and nonexistence of nontrivial solutions for {Choquard} type equations},
     journal = {Electronic Journal of Differential Equations},
     publisher = {mathdoc},
     volume = {2016},
     year = {2016},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2016__2016__a20/}
}
TY  - JOUR
AU  - Wang, Tao
TI  - Existence and nonexistence of nontrivial solutions for Choquard type equations
JO  - Electronic Journal of Differential Equations
PY  - 2016
VL  - 2016
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/EJDE_2016__2016__a20/
LA  - en
ID  - EJDE_2016__2016__a20
ER  - 
%0 Journal Article
%A Wang, Tao
%T Existence and nonexistence of nontrivial solutions for Choquard type equations
%J Electronic Journal of Differential Equations
%D 2016
%V 2016
%I mathdoc
%U http://geodesic.mathdoc.fr/item/EJDE_2016__2016__a20/
%G en
%F EJDE_2016__2016__a20
Wang, Tao. Existence and nonexistence of nontrivial solutions for Choquard type equations. Electronic Journal of Differential Equations, Tome 2016 (2016). http://geodesic.mathdoc.fr/item/EJDE_2016__2016__a20/