Non-degeneracy for the critical Lane-Emden system

Abstract

We prove the non-degeneracy for the critical Lane-Emden system

-Delta U = V-p, -Delta V = U-q, U, V > 0 in R-N

for all N >= 3 and p, q > 0 such that 1/p+1 + 1/q+1 = N-2/N. We show that all solutions to the linearized system around a ground state must arise from the symmetries of the critical Lane-Emden system provided that they belong to the corresponding energy space or they tend to zero at infinity.