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The time evolution of the number density of galaxy clusters and their massand temperature functions are used to constrain cosmological parameters in thespatially flat dark matter models containing a fraction of hot particles(massive neutrino) additional to cold and baryonic matter. We test the modifiedMDM models with cosmic gravitational waves and show that they neither pass thecluster evolution test nor reproduce the observed height of the first acousticpeak in $\Delta T/T$ spectrum, and therefore should be ruled out. The modelswith a non-zero cosmological constant are in better agreement withobservations. We estimate the free cosmological parameters in $\Lambda$MDM witha negligible abundance of gravitational waves, and find that within theparameter ranges $h\in (0.6, 0.7)$, $n\in (0.9, 1.1)$, (i) the value of$\Omega_\Lambda$ is strongly affected by a small fraction of hot dark matter,$f_\nu\equiv\Omega_\nu /\Omega_m\in (0, 0.2)$: $0.45 <\Omega_\Lambda <0.7$($1\sigma$ CL), and (ii) the redshift evolution of galaxy clusters alonereveals the following explicit correlation between $\Omega_\Lambda$ and$f_\nu$: $\Omega_\Lambda +0.5f_\nu =0.65\pm 0.1$. The present accuracy ofobservational data allows only to bound the fraction of hot matter, $f_\nu\in(0, 0.2)$ (the number of massive neutrino species remains undelimited, $N_\nu=1, 2, 3$).Comment: 9 pages, 7 figures, submitted in A&

Abundance and evolution of galaxy clusters in cosmological models with massive neutrino