Stability of the solution of a special type of self-consistent problem

In preceding studies by the present author, it has been shown that in quantum mechanics formulated in the framework of the K-field formalism, Lyapunov-stable solutions of the equations of K-motions describing the dynamics of a test point particle which models the behavior of a microscopic particle from the standpoint of classical mechanics may be selected as the quantization criterion. The present article is concerned with methods of obtaining a stability condition in explicit form.