Large energy entire solutions for the Yamabe equation

AbstractWe consider the Yamabe equation Δu+n(n−2)4|u|4n−2u=0 in Rn, n⩾3. Let k⩾1 and ξjk=(e2jπik,0)∈Rn=C×Rn−2. For all large k we find a solution of the form uk(x)=U(x)−∑j=1kμk−n−22U×(μk−1(x−ξj))+o(1), where U(x)=(21+|x|2)n−22, μk=cnk2 for n⩾4, μk=ck2(logk)2 for n=3 and o(1)→0 uniformly as k→+∞