  This paper is devoted to a dispersion analysis of a class of perturbed
p-Laplacians. Besides the p-Laplacian-like eigenvalue problems we also deal
with new and non-standard eigenvalue problems, which can not be solved by the
methods used in nonlinear eigenvalue problems for p-Laplacians and similar
operators. Original techniques are suggested for solving these new problems
(see Section 3). In addition, dispersion relations between the
eigen-parameters, quantitative analysis of eigenvectors and variational
principles for eigenvalues of perturbed p-Laplacians are also studied in this
paper. The problems, we study in this paper arise from the real world problems.
