The analytical solutions of the density perturbation equation in the Friedman--Lema{i}tre--Robertson--Walker (FLRW) open cosmological models with radiation and positive cosmological constant are provided. The perturbations are of two types: the first propagating as acoustical waves, and the second of non-wave nature. It is shown that there occurs dispersion on curvature and cosmological constant for acoustical perturbations. The wave solutions have anomalous dispersion.

PACS numbers: 98.80.--k, 04.40.--b