The sharpness of some results on stable solutions of −Δu=f(u) in RN

In this note we give a complete answer to a question raised by Dupaigne and Farina (2009) [8] related to the existence of nonconstant stable solutions of the equation −Δu=f(u) in RN, where N≤9 and f is a very general non-negative, non-decreasing and convex nonlinearity.