We investigate the solvability of the Neumann problem (1.1) involving the critical Sobolev nonlinearity with an indefinite weight function and the Hardy potential. We prove that there exists $\lambda^*>0$ such that for $\lambda \in (0,\lambda^*)$, problem (1.1) admits at least two distinct solutions.
"The critical Neumann problem for semilinear elliptic equations with the Hardy potential." Adv. Differential Equations 13 (3-4) 323 - 348, 2008.