Positive radial solutions for Dirichlet problems in the ball

We are concerned with existence, localization and multiplicity of positive radial solutions to Dirichlet problems with Ø-Laplacians in a ball, in both scalar and system cases. Our approach essentially relies on fixed point index computations and a main feature is that it avoids any Harnack type inequality. Applications to some problems involving operators with Uhlenbeck structure are discussed.