  Using the microscopic formalism of Eilenberger equations, a three-band
Ginzburg-Landau theory for the intraband dirty limit and clean interband
scattering case is derived. Within the framework of this three-band
Ginzburg-Landau theory, expressions for the critical temperature Tc and the
temperature dependence of the upper critical field H_c2 are obtained. Based on
some special cases of the matrix of interaction constants, we demonstrate the
influence of the sign of the interband interaction on the critical temperature
and the upper critical field as compared with a two-band superconductor where
it plays no role. We study also analytically and numerically the effect of its
magnitude.
