Classification of nonnegative solutions to static Schrödinger–Hartree and Schrödinger–Maxwell equations with combined nonlinearities

In this paper, we are concerned with static Schrödinger–Hartree and Schrödinger–Maxwell equations with combined nonlinearities. We derive the explicit forms for positive solution u in the critical case and non-existence of nontrivial nonnegative solutions in the subcritical cases (see Theorems 1.1, 1.3). The arguments used in our proof is a variant (for nonlocal nonlinearity) of the direct moving spheres method for fractional Laplacians in Chen et al. (J Funct Anal 272(10):4131–4157, 2017). The main ingredients are the variants (for nonlocal nonlinearity) of the maximum principles, i.e., Narrow region principle (Theorems 2.3, 3.1).