LEAST ENERGY NODAL SOLUTIONS OF THE BREZIS–NIRENBERG PROBLEM IN DIMENSION N = 5

Abstract

We prove the existence of (a pair of) least energy sign changing solutions of [Formula: see text] when Ω is a bounded domain in ℝ N , N = 5 and λ is slightly smaller than λ 1 , the first eigenvalue of -Δ with homogeneous Dirichlet boundary conditions on Ω.