Existence of a ground state solution for Choquard equations involving critical Sobolev exponents
Volume 122 / 2019
Annales Polonici Mathematici 122 (2019), 165-179
MSC: Primary 35A15, 35J61; Secondary 35B09, 35D30, 35B33.
DOI: 10.4064/ap180204-23-11
Published online: 26 April 2019
Abstract
We consider the Choquard equation \begin{equation*} -\varDelta u+u=(I_\alpha*F(u))f(u)+|u|^{2^*-2}u \quad\ \text{in} \ \mathbb{R}^N, \end{equation*} where $N\geq 3$, $\alpha\in (0,N)$, $I_\alpha$ is the Riesz potential and $F(s)=\int_{0}^{s}f(t)\,dt$. If $f$ satisfies the general subcritical growth conditions, we obtain the existence of a positive ground state solution by a variational method.
