Let N >= 3, lambda > 0, beta 0, N + alpha > 0, N + sigma > 0, alpha + 2 > beta, sigma + 2 > beta, beta/2 >= sigma/p(beta,sigma), 1 < q < min(p(beta, sigma)), p(s, t) := 2(N+t)/N+s-2 be the critical Sobolev-Hardy exponent. Via the variational methods, we prove the existence of a nontrivial solution to the singular semilinear problem -div (vertical bar x vertical bar(beta)del u) = vertical bar x vertical bar(alpha) vertical bar u vertical bar(p(beta,alpha)-2)u + lambda a(x)vertical bar u vertical bar(q-2)u, u >= 0 in R-N for suitable parameters N, lambda, q and some kinds of functions a (x). (c)...
