Nonexistence of radial solutions of two elliptic boundary value problems

Abstract

SynopsisWe consider two boundary value problems (of Neumann or related type) associated with the equationin Ω. The existence of a solution was previously established assuming thatp<N/(N−s2). (Ndimension of Ω.) We prove that this exponent is critical for these problems, at least in the radially symmetric case when Ω is a ball. This is understood in the sense that the existence result does not hold whenp≧N/(N− 2).