Constraint minimizers for Choquard equations with different potentials

Abstract

This paper is devoted to the normalized solutions of the Choquard equations and the magnetic Choquard equations involving different external potentials. Under the $L^2$-norm constraint, we apply the variational method and the Gagliardo–Nirenberg-type inequality with the Riesz potential to prove the existence of constraint minimizers of the energy functionals. Particularly, we obtain the compactness of minimizing sequences by establishing the relationship between minimal energies with respect to different mass. We extend and improve the research by Alves and Ji [J. Geom. Anal. 32 (2022), no. 5, article no. 165].