  We formulate a spectral problem related to the onset of superconductivity for
a generalized Ginzburg-Landau model, where the order parameter and the magnetic
potential are defined in the whole space. This model is devoted to the
`proximity effect' for a superconducting sample surrounded by a normal
material. In the regime when the Ginzburg-Landau parameter (of the
superconducting material) is large, we estimate the critical applied magnetic
field for which the normal state will lose its stability, a result that has
some roots in the physical literature. In some asymptotic situations, we
recover results related to the `standard' Ginzburg-Landau model, where we
mention in particular the two-term expansion for the upper critical field
obtained by Helffer-Pan.
