Large solutions of elliptic equations involving critical exponents

1 May 1988

journal article
Published by SAGE Publications in Asymptotic Analysis

Vol. 1 (2) , 139-160
https://doi.org/10.3233/asy-1988-1204

Abstract

We consider positive radial solutions of the equation −Δu=λu^q+u^{(N+2)/(N−2)} 1≤q<(N+2)/(N−2) in the unit ball B in R^N, 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.

Keywords

ELLIPTIC EQUATION
CRITICAL EXPONENT

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