Manifold Method in Eigenvector Theory of Nonlinear Operators

First of all, this work is devoted to studying eigenvectors of nonlinear operators of general form. It is shown that manifolds generated by a family of linear operators are naturally connected with a nonlinear operator. These manifolds are an effective tool for studying the eigenvector problem of nonlinear, as well as linear operators. The description of the properties of the manifolds is of independent interest, and a considerable part of the work is devoted to it.