On infrared behaviour of the gluon propagator

In the framework of gluodynamics the well-known truncated Schwinger–Dyson equation for the gluon propagator is considered. The general case of a power infrared behaviour with non-integer exponents is investigated. The technique of extracting the non-leading terms of the nonlinear integral equation defined only by the infrared behaviour of the propagator is developed. The characteristic equation for the exponent is obtained and the interval of its values $-1\leqslant c\leqslant 3$ is studied. It is shown that the equation for the gluon propagator in question has no solutions with a non-integer and non-halfinteger power infrared behaviour.