Abstract
Abstract In this paper we consider a biharmonic equation of the form Δ2u+V(x)u = f (u) in the whole four-dimensional space ℜ4. Assuming that the potential V satisfies some symmetry conditions and is bounded away from zero and that the nonlinearity f is odd and has subcritical exponential growth (in the sense of an Adams’ type inequality), we prove a multiplicity result. More precisely we prove the existence of infinitely many nonradial sign-changing solutions and infinitely many radial solutions in H2(ℜ4). The main difficulty is the lack of compactness due to the unboundedness of the domain ℜ4 and in this respect the symmetries of the problem play an important role.
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