Large solutions of elliptic equations involving critical exponents

Article type: Research Article

Authors: Atkinson, F.V.^; | Peletier, L.A.

Affiliations: Department of Mathematics, University of Toronto, Toronto M5S 1A1, Ontario, Canada | Mathematical Institute, University of Leiden, 2300 RA Leiden, The Netherlands

Note: [] The authors gratefully acknowledge support from the National Sciences and Engineering Research Council of Canada under Grant A 3979, NATO under Grant 15186 and Argonne National Laboratory.

Abstract: We consider positive radial solutions of the equation −Δu=λuq+u(N+2)/(N−2) 1≤q<(N+2)/(N−2) in the unit ball B in RN, which vanish on the boundary. For c>0, let λ(c) and u(·,c) as denote the eigenvalue and eigenfunction with the property that u(0,c)=c. In this paper we obtain precise estimates for λ(c) and u(·,c) as c tends to infinity.

DOI: 10.3233/ASY-1988-1204

Journal: Asymptotic Analysis, vol. 1, no. 2, pp. 139-160, 1988