Multiple positive solutions for a nonlinear elliptic equation involving Hardy-Sobolev-Maz.ya term

In this paper, we study the existence and nonexistence of multiple positive solutions for the following problem involving Hardy-Sobolev-Maz.ya term: $ - \Delta u - \lambda \frac{u} {{|y|^2 }} = \frac{{|u|^{p_t - 1} u}} {{|y|^t }} + \mu f(x),x \in \Omega ,$ where . is a bounded domain in .N (N . 2), 0 . ., x = (y, z) . .k . .N-k and pt=N+2.2tN.2(0.t.2) For f(x) . C 1(..){0}, we show that there exists a constant .* > 0 such that the problem possesses at least two positive solutions if . . (0, .*) and at least one positive solution if . = .*. Furthermore, there are no positive solutions if . . (.*,+.).