  We investigate the phase diagrams of theoretical models describing bosonic
atoms in a lattice in the presence of randomly localized impurities. By
including multiband and nonlinear hopping effects we enrich the standard model
containing only the chemical-potential disorder with the site-dependent hopping
term. We compare the extension of the MI and the BG phase in both models using
a combination of the local mean-field method and a Hartree-Fock-like procedure,
as well as, the Gutzwiller-ansatz approach. We show analytical argument for the
presence of triple points in the phase diagram of the model with
chemical-potential disorder. These triple points however, cease to exists after
the addition of the hopping disorder.
