Implicit function method in solving a two-dimensional nonlinear spectral problem

Abstract

1. Nonlinear spectral problems arise in various areas of analysis and mathematical physics. Most developed are the theory andmethods of solving such problemswith one-dimensional spectral parameter (see [1–9]). In this paper, we consider a nonlinear spectral problemwith two-dimensional spectral parameter. The use of implicit function methods allows us to study qualitative characteristics of the existing spectrum of holomorphic operator-functions and to construct comparatively simple algorithms for numerical finding of spectral lines or connected components of spectral domains.