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Existence of a ground state solution for Choquard equations involving critical Sobolev exponents

Volume 122 / 2019

Gui-Dong Li, Chun-Lei Tang 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.

Authors

  • Gui-Dong LiSchool of Mathematics and Statistics
    Southwest University
    400715 Chongqing, People’s Republic of China
    e-mail
  • Chun-Lei TangSchool of Mathematics and Statistics
    Southwest University
    400715 Chongqing, People’s Republic of China
    e-mail

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