Abstract
This article is devoted to the existence and multiplicity to the following singular elliptic equation with singular nonlinearities, Hardy-Sobolev critical exponent and weights:
{-Delta u-mu u/vertical bar x vertical bar(2) = vertical bar u vertical bar(p-2)u/vertical bar x vertical bar(s )+ lambda u/vertical bar x vertical bar(alpha)vertical bar mu vertical bar(-)(beta), x is an element of Omega,
u > 0 x is an element of Omega,
u = 0 x is an element of partial derivative Omega.
where Omega is a smooth bounded domain in R-N (N >= 3), 0 is an element of Omega, lambda > 0, 0 <= mu < <(mu)over bar>(N) := (N - 2)(2)/4 , p = 2*(s)=2 (N - s) / (N - 2) with 0 < s < 2 is the critical Hardy-Sobolev critical exponent, 0 <= alpha < N (p -1+ beta)/p , 0 < beta < 1 and 2 < p <= 2* :- 2N/(N - 2) is the critical Sobolev exponent.