Solutions for a singular critical growth problem with a weight

In this paper, we consider some semilinear elliptic equations with Hardy potential. By using linking theorem in [P. Rabinowitz, Minimax Methods in Critical Points Theory with Applications to Differential Equations, CBMS Reg. Conf. Ser. Math., vol. 65, Amer. Math. Soc., Providence, RI, 1986] and analyzing the effect of nonlinearities, we establish the existence of nontrivial solutions.