Oscillatory radial solutions for subcritical biharmonic equations

It is well known that the biharmonic equation ∆^2 u = u|u|^(p-1) with p ∈ (1,∞) has positive solutions on R^n if and only if the growth of the nonlinearity is critical or supercritical. We close a gap in the existing literature by proving the existence and uniqueness, up to scaling and symmetry, of oscillatory radial solutions on R^n in the subcritical case. Analyzing the nodal properties of these solutions, we also obtain precise information about sign-changing large radial solutions and radial solutions of the Dirichlet problem on a ball.