Existence and multiplicity of nontrivial solutions for semilinear elliptic equations involving Hardy-Sobolev critical exponents

A class of semi-linear elliptic equations with critical Hardy-Sobolev exponent has been considered. This model is widely used in hydrodynamics and glaciology, gas combustion in thermodynamics, quantum field theory and statistical mechanics, as well as gravity balance problems in galaxies. The (PS) ₂ sequence of energy functional has been investigated, and then the mountain pass lemma was used to prove the existence of at least one nontrivial solution. Also a multiplicity result has been obtained. Some known results have been generalized.