Nonexistence of multi-bubble solutions for a higher order mean field equation on convex domains

Abstract

In this note, we are concerned with the blowing-up behavior of solutions to the 2p-th order mean field equation under the Navier boundary condition: (Formula presented.) where Ω is a smooth bounded domain in ℝ2p for p ∈ ℕ. By using a new Pohozaev type identity for the Green function of (−Δ)p under the Navier boundary condition, we show that the set of blow up points for any blowing-up solution sequence must be a singleton on convex domains, under some assumptions on the weight function V.