This article is devoted to the study of a perturbation with a viscosity termin an elliptic equation involving the p-Laplacian operator and related tothe best contant problem in Sobolev inequalities in the critical case.We prove first that this problem, together with the equation, is stableunder this perturbation, assuming some conditions on the datas. In thenext section, we show that the zero solution is strongly isolated in somesense, among the space of the solutions. Actually, we end the paper bygiving some analoguous results in the case where the datas presentsymmetries.
