Liouville theorems for nonnegative solutions to weighted Schrödinger equations with logarithmic nonlinearities

In this paper, we are concerned with the physically interesting static weighted Schrödinger equations involving logarithmic nonlinearities:Here we point out the above equations involving higher-order or higher-order fractional Laplacians.We first derive the Liouville theorems (i.e., non-existence of nontrivial nonnegative solutions) in the subcritical-order cases (see Theorem 1.1) via the method of scaling spheres.Secondly, we obtain the Liouville-type results in critical and supercritical-order cases (see Theorem 1.2) by using some integral inequalities.As applications, we also derive Liouville-type results for the Schrödinger system involving logarithmic nonlinearities (see Theorem 1.4).