A Biharmonic Equation in ℜ4 Involving Nonlinearities with Subcritical Exponential Growth

In this paper we consider a biharmonic equation of the form Delta(2)u+V(x)u = f(u) in the whole four-dimensional space R-4. 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 H-2(R-4). The main difficulty is the lack of compactness due to the unboundedness of the domain R-4 and in this respect the symmetries of the problem play an important role.