Singular limit of radial solutions in an annulus

Article type: Research Article

Authors: Gladiali, Francesca^; | Grossi, Massimo

Affiliations: Struttura dipartimentale di Matematica e Fisica, Università di Sassari, via Vienna 2, 07100 Sassari, Italy. E-mail: fgladiali@uniss.it | Dipartimento di Matematica, Università di Roma “La Sapienza”, P. le A. Moro, 2-00185 Roma, Italy. E-mail: grossi@mat.uniroma1.it

Note: [] Corresponding author.

Abstract: In this paper we study the radial solutions of the problem \[\cases{-\Delta u=\lambda\mathrm{e}^{u}& \mbox{in} \varOmega,\cr u=0& \mbox{on} \partial\varOmega,}\] where Ω is an annulus of RN, N≥2 and λ is close to zero. Among the other results we show the existence of a singular limit and some qualitative properties of the solution.

Journal: Asymptotic Analysis, vol. 55, no. 1-2, pp. 73-83, 2007