On the One Method of Analyzing the Stability of Rest Points in Critical Cases

Abstract

For a two-dimensional oscillatory system with imaginary characteristic roots of linearized equations, a method is proposed that simplifies calculations and does not require the analyticity of the right-hand sides of the equations. The method is based on the decomposition of the vector function of the right-hand sides of the equations into solenoidal and potential components. Integral estimates for the stability of the equilibrium position are obtained.