On The Existence Of Multiple Solutions For A Singular Elliptic Equation Involving Critical Sobolev-hardy Exponents In RN

In this master’s dissertation, we study the singular elliptic equation involv-ing multi-singular inverse square potentials and critical Sobolev-Hardy expo-nents and derive the existence of infinitely many solutions. Where0≤μi≤μ=(N-2/2)2,0≤s<2,1<q<2,0<a(x)∈Lq’(RN), ai∈RN, moreover, ai are differen-t,i=1:2,…,k≤N,2*is critical Sobolev-Hardy exponent. We first prove a slight variant of concentration compactness prin-ciple, by means of the principle and minimax principle, and the Z2index theorem, we obtain infinitely many solutions for suitable positive parameters αi,i,=1,2,…,k,β.