Stability of a second-order differential equation with retarded argument

Effective criteria for exponential stability of second-order linear equations based on the positivity of the Cauchy function are proposed. Bounds of the ‘smallness’ of the deviation of the argument are established under which the equation with retarded argument is still stable if the ordinary differential equation with the same coefficients is stable. Based on the criteria obtained, an applied problem on the regulation of concentration is analyzed.