Existence of nontrivial weak solutions for a quasilinear Choquard equation.

We are concerned with the following quasilinear Choquard equation: [Formula: see text] where [Formula: see text], [Formula: see text] is the p-Laplacian operator, the potential function [Formula: see text] is continuous and [Formula: see text]. Here, [Formula: see text] is the Riesz potential of order [Formula: see text]. We study the existence of weak solutions for the problem above via the mountain pass theorem and the fountain theorem. Furthermore, we address the behavior of weak solutions to the problem near the origin under suitable assumptions for the nonlinear term f.