Existence of Solutions for Singular Critical Growth Semilinear Elliptic Equations

A semilinear elliptic problem containing both a singularity and a critical growth term is considered in a bounded domain of n: existence results are obtained by variational methods. The solvability of the problem depends on the space dimension n and on the coefficient of the singularity; the results obtained describe the behavior of critical dimensions and nonresonant dimensions when the Brezis–Nirenberg problem is modified with a singular term.