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The problem of stability of saturated and non-saturated ferromagnetism in theHubbard model is considered in terms of the one-particle Green's functions.Approximations by Edwards and Hertz and some versions of the self-consistentapproximations based on the 1/z-expansion are considered. The account oflongitudinal fluctuations turns out to be essential for description of thenon-saturated state. The corresponding pictures of density of states areobtained. "Kondo" density-of-states singularities owing to spin-flip processesare analyzed. The critical electron concentrations for instabilities ofsaturated ferromagnetism and paramagnetic state are calculated for variouslattices. Drawbacks of various approximations are discussed. A comparison withthe results of previous works is performed.Comment: 16 pages, 7 eps figure

Density-of-states picture and stability of ferromagnetism in the highly correlated Hubbard model