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.

A Biharmonic Equation in ℜ4 Involving Nonlinearities with Subcritical Exponential Growth / F. Sani. - In: ADVANCED NONLINEAR STUDIES. - ISSN 1536-1365. - 11:4(2011 Nov), pp. 889-904. [10.1515/ans-2011-0407]

A Biharmonic Equation in ℜ4 Involving Nonlinearities with Subcritical Exponential Growth

F. Sani
Primo
2011

Abstract

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.
biharmonic operator; exponential growth; Trudinger-Moser inequalities; variational methods
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/2434/501390
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