On a semilinear elliptic equation with singular term and Hardy–Sobolev critical growth

In a previous work [6], we got an exact local behavior to the positive solutions of an elliptic equation. With the help of this exact local behavior, we obtain in this paper the existence of solutions of an equation with Hardy–Sobolev critical growth and singular term by using variational methods. The result obtained here, even in a particular case, relates with a partial (positive) answer to an open problem proposed in: A. Ferrero and F. Gazzola, Existence of solutions for singular critical growth semilinear elliptic equations, J. Differential Equations 177 , 494–522 (2001). (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)