Behavior at infinity of solutions of an equation of Osserman–Keller type ✩

We study the behavior at infinity of solutions of equations of the form Δu = up, where p >1, in dimensions n 3. In particular we extend results proved by Loewner and Nirenberg in Contribution to Analysis, 1974, pp. 245–272 for the case p = (n + 2)/(n − 2), n 3, to values of p in the range p >n/(n−2), n 3.  2003 Elsevier Inc. All rights reserved