In this paper we present some results for mixed sublinear superlinear critical problem in dimension
In some special cases this problem is known as the Brezis-Nirenberg equation. We study the existence of solutions and analyse all subcritical, critical and supercritical cases for the possible singularities of radial solutions at the origin. The solutions lie on three sets. There are bounded solutions with a finite number of nodes in
singular at the origin still with finite number of zeros in
and singular with sign-changing oscillations at the origin.
Keywords and phrases:
Brezis-Nirenberg problem, Emden-Fowler transform, energy functional, Pohozhaev identity.
