A biharmonic equation in □4involving nonlinearities with critical exponential growth

摘要

In this paper we give sufficient conditions for the existence of so- lutions of a biharmonic equation of the form (equation required) where V is a continuous positive potential bounded away from zero and the nonlinearity f(s) behaves like e_(α0s2) at infinity for some α_0 > 0. In order to overcome the lack of compactness due to the unboundedness of the domain □4, we require some additional assumptions on V. In the case when the potential V is large at infinity we obtain the existence of a nontrivial solution, while requiring the potential V to be spherically symmetric we obtain the existence of a nontrivial radial solution. In both cases, the main difficulty is the loss of compactness due to the critical exponential growth of the nonlinear term f.