Infinitely Many Solutions for a Nonlinear Elliptic PDE with Multiple Hardy-Sobolev Critical Exponents

In this paper, by an approximating argument, we obtain two disjoint and infinite sets of solutions for the following elliptic equation with multiple Hardy-Sobolev critical exponents {-Delta u = mu vertical bar u vertical bar(2*-2)u + Sigma(l)(i-1) vertical bar u vertical bar(2*(si)-2)u/vertical bar x vertical bar(si) + a(x)vertical bar u vertical bar(q-2)u in Omega, u=0 on partial derivative Omega, where omega is a smooth bounded domain in R-N with 0 is an element of partial derivative Omega and all the principle curvatures of partial derivative Omega; at 0 are negative, a is an element of C-1((Omega) over bar ,R*(+)), mu > 0, 0 < s(1) < s(2) < ... < s(l) < 2, 1 < q < 2 and N > 2q+1/q-1. By 2* :=2N/N-2 and 2*(s(i)) :=2(N-s(i))/N-2 we denote the critical Sobolev exponent and Hardy-Sobolev exponents, respectively