Existence of stable standing waves for the fractional Schrödinger equations with combined power-type and Choquard-type nonlinearities

Abstract

In this paper, we study the orbital stability of standing waves for the fractional Schrödinger equations with combined power-type and Choquard-type nonlinearities. By using variational methods, when one nonlinearity is focusing and L2-critical, the other is defocusing and L2-supercritical, we prove that there exist the orbitally stable standing waves. We extend the results of Bhattarai [J. Differ. Equations 263, 3197–3229 (2017)] and Feng-Zhang [Comput. Math. Appl. 75, 2499–2507 (2018)] to the L2-critical and L2-supercritical nonlinearities.