Liouville theorems for stable radial solutions for the biharmonic operator

Article type: Research Article

Authors: Warnault, Guillaume

Affiliations: LMPT CNRS UMR 6083, Université Francois Rabelais, Parc Grandmont, 37200 Tours, France. E-mail: [email protected]

Abstract: This article is concerned with the non-existence of stable solutions for a fourth-order semilinear elliptic equation Δ2u=f(u) in RN, where f is a smooth nonlinearity. We establish the non-existence of stable radial solutions which verify decay conditions at infinity. Our Liouville-type results do not depend on the specific nonlinearity f. Moreover, in low dimensions and under no radial symmetry assumption, we prove Liouville-type results when f is increasing.

Keywords: biharmonic operator, Liouville result

DOI: 10.3233/ASY-2010-0997

Journal: Asymptotic Analysis, vol. 69, no. 1-2, pp. 87-98, 2010