Existence and nonexistence results of a problem involving the pseudobilaplacian operator

Abstract

In this paper we obtain some existence and nonexistence results of a problem involving the pseudobilaplacian operator. By the sub and supersolutions techniques we prove that the problem admits a positive solution when it is subhomogeneous. In the case where it is superhomogeneous, we prove the existence of nontrivial solutions. The nonexistence result follows from a Pohozaev-type identity.