Existence and Uniqueness of Fast Decay Entire Solutions of Quasilinear Elliptic Equations

We prove the existence and uniqueness of fast decay solutions and clarify the structure of positive radial solutions of the quasilinear elliptic equation Δmu+f(u)=0 in n, where Δm denotes the m-Laplace operator, and f has a supercritical growth for small u>0 and a subcritical growth for large u. Our proofs use only elementary arguments based on several variational identities and a maximum principle of Peletier and Serrin.