Geodesic
Existence and nonexistence of nontrivial solutions for Choquard type equations
Electronic journal of differential equations, Tome 2016 (2016)
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},
     year = {2016},
     volume = {2016},
     zbl = {1333.35027},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2016__2016__a20/}
}
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TI  - Existence and nonexistence of nontrivial solutions for Choquard type equations
JO  - Electronic journal of differential equations
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VL  - 2016
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LA  - en
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%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
%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/