Construction of sign-changing solutions for a harmonic equation with subcritical exponent

Abstract

In this paper, we study the harmonic equation involving subcritical exponentunit ball in R n , n ≥ 5 with Euclidean metric g 0 , ∂B n = S n−1 is its boundary, K is a function on S n−1 and ε is a small positive parameter. We construct solutions of the subcritical equation (P ε ) which blow up at two different critical points of K . Furthermore, we construct solutions of (P ε ) which have two bubbles and blow up at the same critical point of K .