Liouville-type theorems for the fourth order nonlinear elliptic equation.

Abstract: In this paper, we are concerned with Liouville-type theorems for the nonlinear elliptic equation where , and is an unbounded domain of , . We prove Liouville-type theorems for solutions belonging to one of the following classes: stable solutions and finite Morse index solutions (whether positive or sign-changing). Our proof is based on a combination of the Pohozaev-type identity, monotonicity formula of solutions and a blowing down sequence, which is used to obtain sharp results. [Copyright &y& Elsevier]