Multiple solutions for weighted nonlinear elliptic system involving critical exponents

This paper deals with the existence and multiplicity of nontrivial solutions for a weighted nonlinear elliptic system involving critical exponents and singular potentials in a bounded domain. By using the Caffarelli–Kohn–Nirenberg inequality and variational method, we prove that the system has at least two nontrivial solutions when the pair of parameters (λ,δ)(λ,δ) belongs to a certain subset of R2R2.