Symmetry and Monotonicity of Positive Solutions for a Class of Choquard Equation with Hardy Potential

In this paper, a class of Choquard equation with Hardy potential in the whole space ℝ N will be considered, where the parameters p , q and α in the convolution-nonlinearity term are under a suitable range. Without the hypothesis of pointwise decay estimates for solutions, the symmetry of positive solutions in D 1,2 ( ℝ N )∩C( ℝ N \{ 0 } ) to such an equation is obtained via some subtle integral estimates and moving plane techniques.