  Cold dark matter models predict the existence of a large number of
substructures within dark matter halos. If the cold dark matter consists of
weakly interacting massive particles, their annihilation within these
substructures could lead to diffuse GeV emission that would dominate over the
annihilation signal of the host halo. In this work we search for GeV emission
from three nearby galaxy clusters: Coma, Virgo and Fornax. We first remove
known extragalactic and galactic diffuse gamma-ray backgrounds and point
sources from the Fermi 2-year catalog and find a significant residual diffuse
emission in all three clusters. We then investigate whether this emission is
due to (i) unresolved point sources; (ii) dark matter annihilation; or (iii)
cosmic rays (CR). Using 45 months of Fermi-LAT data we detect several new point
sources (not present in the Fermi 2-year point source catalogue) which
contaminate the signal previously analyzed by Han et al.(arxiv:1201.1003).
Including these and accounting for the effects of undetected point sources, we
find no significant detection of extended emission from the three clusters
studied. Instead, we determine upper limits on emission due to dark matter
annihilation and cosmic rays. For Fornax and Virgo the limits on CR emission
are consistent with theoretical models, but for Coma the upper limit is a
factor of 2 below the theoretical expectation. Allowing for systematic
uncertainties associated with the treatment of CR, the upper limits on the
cross section for dark matter annihilation from our clusters are more stringent
than those from analyses of dwarf galaxies in the Milky Way. We rule out the
thermal cross section for supersymmetric dark matter particles for masses as
large as 100 GeV (depending on the annihilation channel).
