On a fourth order elliptic equation with supercritical exponent

Abstract

This paper is concerned with the semi-linear elliptic problem involving nearly critical exponent (P ε ):where is a smooth bounded domain in R n , n ≥ 5, and ε is a positive real parameter. We show that, for ε small, (P ε ) has no sign-changing solutions with low energy which blow up at exactly three points. Moreover, we prove that (P ε ) has no bubble-tower sign-changing solutions. MSC: 35J20; 35J60

Sign-changing bubble tower solutions for a Paneitz-type problem

“…Concerning the supercritical case, namely q = N+4 N−4 + ε with ε > 0, when K is a constant, Bouh [6] showed that there is no sign-changing solution with low energy which blow up at exactly two points for ε small and proved that problem (1.3) has no bubble-tower sign-changing solutions. Ayed and Mehdi [4] got that the supercritical problem (1.3) has no solutions which concentrate around a point of Ω as ε → 0.…”