We consider the following nonlinear problem & nbsp;-delta u + V (|y|)u = u(p), u > 0 in R-N, u is an element of H-1(R-N), (0.1)& nbsp;where V (r) is a positive function, 1 < p < N+2/N-2. We show that the multi-bump solutions constructed in [27] are non-degenerate in a suitable symmetric space. We also use this non-degenerate result to construct new solutions for (0.1)....
