The Nehari manifold approach for multiplicity of positive solutions to semilinear elliptic system involving multi-singular inverse square potentials with Sobolev critical exponent

Using the Nehari manifold and variational methods, the existence and multiplicity of positive solutions for the multi-singular semilinear elliptic system with critical growth terms in bounded domains are investigated. In addition, under appropriate assumptions, it is shown that the system has at least two positive solutions when the pair of the parameters (α,β) belongs to a certain subset of R2.