Multiple perturbations of a singular eigenvalue problem

We study the perturbation by a critical term and a (p-1)-superlinear subcritical nonlinearity of a quasilinear elliptic equation containing a singular potential. By means of variational arguments and a version of the concentration-compactness principle in the singular case, we prove the existence of solutions for positive values of the parameter under the principal eigenvalue of the associated singular eigenvalue problem. (C) 2014 Elsevier Ltd. All rights reserved.