Abstract
This paper is devoted to the study of the nonlinear elliptic problem with supercritical critical exponent (Pε) : −Δu = K|u|4/(n−2)+εu in Ω, u = 0 on ∂Ω, where Ω is a smooth bounded domain in ℝn, n ≥ 3, K is a C3 positive function and ε is a positive real parameter. We show first that in dimension 3, for ε small, (Pε) has no sign-changing solutions with low energy which blow up at two points. For n ≥ 4, we prove that there are no sign-changing solutions which blow up at two nearby points. We also show that (Pε) has no bubble-tower sign-changing solutions.
Published Online: 2016-03-10
Published in Print: 2012-02-01
© 2016 by Advanced Nonlinear Studies, Inc.
