Abstract

For the equation- ? u + u - ß = u p, u > 0 in B R, u = 0 on ? B R, where B R ? R N, 0 < ß < 1 and 1 < p < frac(N + 2, N - 2) if N = 3, 1 < p < + 8 if N = 2, we show that there is over(R, ¯) > 0 such that a radial solution u R exists if and only if 0 < R = over(R, ¯). It is unique in the class of radial solutions and u R ' (R) < 0 if R < over(R, ¯), while u over(R, ¯) ' (over(R, ¯)) = 0. We also give a variational characterization of u over(R, ¯). © 2008 Elsevier Inc. All rights reserved.