ABSTRACT
So far, we have mostly dealt with stable solutions of (1.3) for two specific types of domains: Ω is bounded or Ω = RN . In this section, we review a number of results applying to other geometries.
The Lane-Emden nonlinearity
We begin discussing (1.3) for Ω = RN+ in the case of the Lane-Emden nonlinearity. ¨−∆u= |u|p−1u in RN+,
u= 0 on ∂RN+. (8.1)
When p is subcritical, no positive solution exists.
