Asymptotics for semilinear elliptic equations with supercritical nonlinearities in annular domains

Article type: Research Article

Authors: Budd, C.J. | Peletier, L.A.^;

Affiliations: School of Mathematics, University of Bristol, Bristol, UK | Mathematical Institute, Leiden University, Leiden, The Netherlands

Note: [] Correspondence to: L.A. Peletier, Department of Mathematics and Computer Science, Leiden University, P.O. Box 9512, 2300 RA Leiden, The Netherlands.

Abstract: We study radially symmetric solutions of the equation Δu+up=0 in annular domains {a<|x|<1} in R3. In particular we are interested in the behaviour of solutions when the power p tends to the critical Sobolev exponent 5 in R3 and simultaneously, the inner radius shrinks to zero. When p$\searrow$5, two forms of behaviour are observed, depending on whether (p−5)2«a or a«(p−5)2.

DOI: 10.3233/ASY-1993-6302

Journal: Asymptotic Analysis, vol. 6, no. 3, pp. 219-239, 1993