In this paper we consider the problem where p > 1 and Ω R is a smooth bounded domain with a hole which is diffeomorphic to an annulus and expands asR → ∞. The main goal of the paper is to prove, for large R, the existence of a positive solution to (0.1) which is close to the positive radial solution in the corresponding diffeomorphic annulus. The proof relies on a careful analysis of the spectrum of the linearized operator at the radial solution as well as on a delicate analysis of the nondegeneracy of suitable approximating solutions. © 2011 Springer-Verlag.
Asymptotically radial solutions in expanding annular domains / Thomas, Bartsch; Monica, Clapp; Grossi, Massimo; Pacella, Filomena. - In: MATHEMATISCHE ANNALEN. - ISSN 0025-5831. - STAMPA. - 352:2(2012), pp. 485-515. [10.1007/s00208-011-0646-3]
Asymptotically radial solutions in expanding annular domains
GROSSI, Massimo;PACELLA, Filomena
2012
Abstract
In this paper we consider the problem where p > 1 and Ω R is a smooth bounded domain with a hole which is diffeomorphic to an annulus and expands asR → ∞. The main goal of the paper is to prove, for large R, the existence of a positive solution to (0.1) which is close to the positive radial solution in the corresponding diffeomorphic annulus. The proof relies on a careful analysis of the spectrum of the linearized operator at the radial solution as well as on a delicate analysis of the nondegeneracy of suitable approximating solutions. © 2011 Springer-Verlag.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.