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

DOI: 10.4236/jamp.2025.133046, PP. 871-888

Keywords: Choquad Equation, Hardy Potential, Positive Solutions, Moving Plane Method

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Abstract:

In this paper, a class of Choquard equation with Hardy potential in the whole space ？ 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 ( ？ N )∩C( ？ N \{ 0 } ) to such an equation is obtained via some subtle integral estimates and moving plane techniques.

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