Asymptotics for semilinear elliptic equations with supercritical nonlinearities in annular domains
Chris J. Budd, Lambertus A. Peletier · Asymptotic Analysis · 1993
We study radially symmetric solutions of the equation Δu+u p =0 in annular domains {a<|x|<1} in R 3 . In particular we are interested in the behaviour of solutions when the power p tends to the critical Sobolev exponent 5 in R 3 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 .