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 eα0s2 at infinity for some α0 > 0. In order to overcome the lack of compactness due to the unboundedness of the domain ℝ4, 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.
|Titolo:||A biharmonic equation in ℝ4involving nonlinearities with critical exponential growth|
SANI, FEDERICA (Corresponding)
|Parole Chiave:||biharmonic equation; critical exponential growth; Trudinger-Moser inequalities; variational methods; analysis; applied mathematics|
|Settore Scientifico Disciplinare:||Settore MAT/05 - Analisi Matematica|
|Data di pubblicazione:||gen-2013|
|Digital Object Identifier (DOI):||10.3934/cpaa.2013.12.405|
|Appare nelle tipologie:||01 - Articolo su periodico|