Large solutions of elliptic equations involving critical exponents

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.