Normalized solutions for Kirchhoff–Choquard type equations with different potentials

Abstract

In this paper, we are concerned with a Kirchhoff-Choquard type equation with L2-prescribed mass. Under different cases of the potential, we prove the existence of normalized ground state solutions to this equation. To obtain the boundedness from below of the energy functional and the compactness of the minimizing sequence, we apply the Gagliardo-Nirenberg inequality with the Riesz potential and the relationship between the different minimal energies corresponding to different mass. We also extend the results to the fractional Kirchhoff-Choquard type equation.