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We consider minimizers of a Ginzburg-Landau energy with a discontinuous andrapidly oscillating pinning term, subject to a Dirichlet boundary condition ofdegree $d > 0$. The pinning term models an unbounded number of small impuritiesin the domain. We prove that for strongly type II superconductor withimpurities, minimizers have exactly d isolated zeros (vortices). These vorticesare of degree 1 and pinned by the impurities. As in the standard case studiedby Bethuel, Brezis and H\'elein, the macroscopic location of vortices isgoverned by vortex/vortex and vortex/ boundary repelling effects. In somespecial cases we prove that their macroscopic location tends to minimize therenormalized energy of Bethuel-Brezis-H\'elein. In addition, impurities affectthe microscopic location of vortices. Our technics allows us to work withimpurities having different size. In this situation we prove that vortices arepinned by the largest impurities.

The Ginzburg-Landau functional with a discontinuous and rapidly oscillating pinning term. Part II: the non-zero degree case