Eigenvalue problems for some nonlinear perturbations of the Laplace operator by

The study of eigenvalue problems of various differential operators captured an enormous interest in the last decades. A large variety of papers pointed out different phenomena which can occur on the spectrum of certain differential operators. We just remember the recent advances in [3, 4, 5, 7, 8, 9, 10, 11, 12, 15, 16]. The goal of this paper is to point out certain results on an eigenvalue problem in which we perturb the Laplace operator in a sense that will be described later. More exactly, in this paper we are concerned with the study of an eigenvalue problem of the type