For the related research of perturbation system with mixed critical index and subcritical situation, the well-posedness of the local solution is obtained by the variational method.
For the study of the disturbance system of the subcritical situation of the mixed critical index, the appropriate characterization of local solution is obtained by the differential method.
In this paper, we use the variational method to obtain the well posed local solutions for the study of the perturbed system in the subcritical case with mixed critical index.<br>