Liouville theorems for stable radial solutions for the biharmonic operator

This article is concerned with the non-existence of stable solutions for a fourth-order semilinear elliptic equation Δ 2 u = f (u )i nR N ,w heref is a smooth nonlinearity. We establish the non-existence of stable radial solutions which verify de- cay conditions at infinity. Our Liouville-type results do not depend on the specific nonlinearity f . Moreover, in low dimensions and under no radial symmetry assumption, we prove Liouville-type results when f is increasing.