Аннотация:

Currently, the theory of linear operators perturbations has become the completed section of functional analysis, and all the main cases are considered when the initial and disturbing operators can be both limited and unlimited. The decisions are looking in the form of rows along the degrees of the small parameter and the question arises of the nature of the convergence of these ranks. In the presented work, the conditions for the existence of the holomorphic according to the parameter of the solutions were found in the case when the perturbing operator is bilinear.