On symmetric solutions of a critical semilinear elliptic system involving the Caffarelli-Kohn-Nirenberg inequality in R N $\mathbb{R}^{N}$

Abstract This paper deals with the existence and multiplicity of symmetric solutions for a weighted semilinear elliptic system with multiple critical Hardy-Sobolev exponents and singular potentials in R N $\mathbb{R}^{N}$ . Applying the symmetric criticality principle and Caffarelli-Kohn-Nirenberg inequality, we establish several existence and multiplicity results of G-symmetric solutions under certain appropriate hypotheses on the parameters and the weighted functions.