QUALITATIVE PROPERTIES OF SINGULAR SOLUTIONS OF CHOQUARD EQUATIONS

Our aim of this paper is to study qualitative properties of isolated singular solutions to Choquard equation (Formula Presented) where (Formula Presented) is the Dirac mass concentrated at the origin and (Formula Presented). Multiple properties of very weak solutions of (0.1) are considered: (i) to obtain the existence of minimal solutions and extremal solutions for N = 2, which are derived in [8] when N ≥ 3; (ii) to analyze the stability of minimal solutions and the semi stability of extremal solutions; (iii) to derive a second solution by the Mountain Pass theorem when q = p − 1 and N = 2, 3; (iv) to obtain the radial symmetry of the positive singular solutions by the method of moving planes.