UNIQUENESS AND GLOBAL STRUCTURE OF POSITIVE RADIAL SOLUTIONS FOR QUASILINEAR ELLIPTIC EQUATIONS

Using only elementary analysis based on an important identity of Ni, Pucci and Serrin, and a maximum principle of Peletier and Serrin, we completely clarify the structure of positive radial solutions of m-Laplace equations. For a large class of nonlinearities, including polynomial, rational, exponential, logarithmic and trigonometric functions, we can then resolve problems of existence and uniqueness of ground states or positive radial solutions of the associated Dirichlet problem in a ball in R ⁿ .