Large energy entire solutions for the Yamabe equation

Abstract

We consider the Yamabe equation Delta u + n(n-2_/4 vertical bar u vertical bar 4/n-2 u = 0 in R(n), n >= 3. Let k >= 1 and xi(k)(j) = (e(2j pi u/k), 0) is an element of R(n) = C x R(n-2). For all large k we find a solution of the form u(k)(x)= u(x) - Sigma(k)(j=1) mu(k) (-n-2/2) U X (mu(-1)(k) (x - xi(j)) +o(1), where U(x) = (2/1+vertical bar x vertical bar(2)) (n-2/2), mu(k) = c(n)/k(2) for n >= 4, mu k = c/k(2)(logk)(2) for n =3 and o(1) -> 0 uniformly as k -> +infinity. (C) 2011 Elsevier Inc. All rights reserved.