Blow-up and nonexistence of sign changing solutions to the Brezis–Nirenberg problem in dimension three

Abstract

In this paper we study low energy sign changing solutions of the critical exponent problem (Pλ):−Δu=u5+λu in Ω, u=0 on ∂Ω, where Ω is a smooth bounded domain in R3 and λ is a real positive parameter. We make a precise blow-up analysis of this kind of solutions and prove some comparison results among some limit values of the parameter λ which are related to the existence of positive or of sign changing solutions.