Starting from an axisymmetric, differentially rotating thin disc at equilibrium, in which the velocity dispersion is not large and in which the particles are characterized by a mass distribution and by a relationship between mass and velocity dispersion, we consider the stability of such a configuration against small axisymmetric disturbances. The analysis is performed kinetically and the behaviour of the marginal stability curves for different values of the system's parameters is investigated. Specifically, we consider the implications of changes in the parameters characterizing the mass spectrum range and the law relating the mass and velocity dispersion. Our results show that the characteristics of the system can significantly affect the critical stability parameters. We point out that such effects may strongly influence the evolution of the interstellar medium in disc galaxies.