Geodesic
Positive ground state solutions to Schrödinger-Poisson systems with a negative non-local term
Electronic Journal of Differential Equations, Tome 2015 (2015).

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

Summary: In this article, we study the Schrodinger-Poisson system $$\displaylines{ -\Delta u+u-\lambda K(x)\phi(x)u=a(x)|u|^{p-1}u, \quad x\in\mathbb{R}^3, \cr -\Delta\phi=K(x)u^{2},\quad x\in\mathbb{R}^3, }$$ with $p\in(1,5)$. Assume that $a:\mathbb{R}^3\to \mathbb{R^{+}}$ and $K:\mathbb{R}^3\to \mathbb{R^{+}}$ are nonnegative functions and satisfy suitable assumptions, but not requiring any symmetry property on them, we prove the existence of a positive ground state solution resolved by the variational methods.
Classification : 35J47, 35J50, 35J99
Keywords: Schrödinger-Poisson system, ground state solution, variational methods 
@article{EJDE_2015__2015__a70,
     author = {Gao, Yan-Ping and Yu, Sheng-Long and Tang, Chun-Lei},
     title = {Positive ground state solutions to {Schr\"odinger-Poisson} systems with a negative non-local term},
     journal = {Electronic Journal of Differential Equations},
     publisher = {mathdoc},
     volume = {2015},
     year = {2015},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2015__2015__a70/}
}
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Gao, Yan-Ping; Yu, Sheng-Long; Tang, Chun-Lei. Positive ground state solutions to Schrödinger-Poisson systems with a negative non-local term. Electronic Journal of Differential Equations, Tome 2015 (2015). http://geodesic.mathdoc.fr/item/EJDE_2015__2015__a70/