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.

A biharmonic equation in ℝ4involving nonlinearities with critical exponential growth / F. Sani. - In: COMMUNICATIONS ON PURE AND APPLIED ANALYSIS. - ISSN 1534-0392. - 12:1(2013 Jan), pp. 405-428. [10.3934/cpaa.2013.12.405]

A biharmonic equation in ℝ4involving nonlinearities with critical exponential growth

F. Sani
2013

Abstract

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.
biharmonic equation; critical exponential growth; Trudinger-Moser inequalities; variational methods; analysis; applied mathematics
Settore MAT/05 - Analisi Matematica
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/501398
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