Uniqueness and non-degeneracy of positive radial solutions for quasilinear elliptic equations with exponential nonlinearity

We are concerned with the uniqueness and non-degeneracy result of positive solutions for a class of quasilinear elliptic equations with exponential nonlinearity. We convert a quasilinear elliptic equation into a semilinear one and study precise correspondences between two equations. We show the uniqueness and the non-degeneracy of positive solutions by analyzing the converted semilinear problem.