Cauchy's Generalized Problem in Solving a Nonlinear Three-parameter Spectral Problem

The paper proposes a new numerical method for solving a three-parameter nonlinear spectral problem for holomorphic operator-functions, defined in Banach spaces. The concept of a generalized Cauchy problem is introduced, which is to solve a system of two equations in partial first-order derivatives with a common initial condition. This makes it possible to find connected components of spectrum (CCS) in the form of three-dimensional smooth spectral surfaces.