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We explore the implications of possible neutrino oscillations, as indicatedby the solar and atmospheric neutrino experiments, for the cold plus hot darkmatter scenario of large scale structure formation. We find that there areessentially three distinct schemes that can accommodate the oscillation dataand which also allow for dark matter neutrinos. These include (i) three nearlydegenerate (in mass) neutrinos, (ii) non-degenerate masses with $\nu_\tau$ inthe eV range, and (iii) nearly degenerate $\nu_\mu-\nu_\tau$ pair (in the eVrange), with the additional possibility that the electron neutrino iscosmologically significant. The last two schemes invoke a `sterile' neutrinowhich is light (< or ~ eV). We discuss the implications of these schemes for$\bar{\nu}_\mu - \bar{\nu}_e$ and $\nu_\mu - \nu_\tau$ oscillation, and findthat scheme (ii) in particular, predicts them to be in the observable range. Asfar as structure formation is concerned, we compare the one neutrino flavorcase with a variety of other possibilities, including two and three degenerateneutrino flavors. We show, both analytically and numerically, the effects ofthese neutrino mass scenarios on the amplitude of cosmological densityfluctuations. With a Hubble constant of 50 km s$^{-1}$ Mpc$^{-1}$, a spectralindex of unity, and $\Omega_{baryon} = 0.05$, the two and three flavorscenarios fit the observational data marginally better than the single flavorscheme. However, taking account of the uncertainties in these parameters, weshow that it is premature to pick a clear winner.Comment: 1 LaTEX file plus 1 uuencoded Z-compressed tar file with 3 postscript  figure

Cold plus hot dark matter cosmology in the light of solar and atmospheric neutrino oscillations