Fowler transformation and radial solutions for quasilinear elliptic equations. Part 2: nonlinearities of mixed type

We discuss the existence and the asymptotic behavior of positive radial solutions for the following equation: $$Delta_p u( extbf{x})+ f(u,| extbf{x}|)=0,$$ where $Delta_p u=div(|Du|^{p-2}Du)$, $ extbf{x} in mathbb{R}^n$, $n>p>1$, and we assume that $f ge0$ is subcritical for $u$ large and $|mathbf{x}|$ small and supercritical for $u$ small and $|mathbf{x} |$ large, with respect to the Sobolev critical exponent. We give sufficient conditions for the existence of ground states with fast decay. As a corollary we also prove the existence of ground states with slow decay and of singular ground states with fast and slow decay. For the proofs we use a Fowler transformation that enables us to use dynamical arguments. This approach allows to unify the study of different types of nonlinearities and to complete the results already appeared in literature with the analysis of singular solutions.