Concepedia

Ground states and high energy solutions of the planar Schrödinger–Poisson system

Miao Du, Tobias Weth

Nonlinearity · 2017 · 85 citations · 24 references

DOI

Concepts

Abstract

In this paper, we are concerned with the Schrödinger–Poisson system 0.1 {−Δu+u+ϕu=|u|p−2uin Rd,Δϕ=u2in Rd.

References

24

Nonlinear scalar field equations, I existence of a ground state

Henri Berestycki, P. L. Lions · Archive for Rational Mechanics and Analysis · 1983 · 2.6K citations · Full text

, , +13

Sharp Constants in the Hardy-Littlewood-Sobolev and Related Inequalities

Élliott H. Lieb · Annals of Mathematics · 1983 · 1.1K citations

, , +9

Existence of solutions with prescribed norm for semilinear elliptic equations

Louis Jeanjean · Nonlinear Analysis · 1997 · 767 citations

, , +10

The Schrödinger–Poisson equation under the effect of a nonlinear local term

David Ruiz · Journal of Functional Analysis · 2006 · 758 citations

, , +14

Nonlinear scalar field equations

W. Rother · Differential and Integral Equations · 1992 · 599 citations · Full text

, , +12