Classification of the Solutions of Semilinear Elliptic Problems in a Ball

In this paper we fully describe the set of the positive and nodal (regular and singular) radial solutions of the superlinear elliptic PDE. −Δu=λu+up−1 u in B1, u=0 on ∂B1, p>1, (1)without restriction on the range of λ . Here, B1 is the unit ball in N. More precisely, in all subcritical, critical and supercritical cases, we analyze the possible singularities of radial solutions at the origin and the number of bounded and unbounded solutions. The solutions will be of three different types: bounded with a finite number of zeroes in (0, 1), singular at the origin, still with a finite number of zeroes and singular with sign changing oscillations at the origin