We study distributional solutions of semilinear biharmonic equations of the type
Δ2u+f(u)=0 onRN,
where f is a continuous function satisfying f (t)t ≥ c |t|q+1 for all t ∈ R with c > 0 and q > 1. By using a new approach mainly based on careful choice of suitable weighted test functions and a new version of Hardy- Rellich inequalities, we prove several Liouville theorems independently of the dimension N and on the sign of the solutions.
