Instability of bound states for 2d nonlinear Schrodinger equations

We study standing wave solutions of the form 3(i(ω t+mθ))φ(r) to nonlinear Schrodinger equation iu(t) + Δ u + | u|(p-1)u=0 for x ∈ R-2 and t > 0, where (r, θ) are polar coordinates and m ∈ N. Using the Evans function, we prove linear instability of standing wave solutions with nodes in the case where p > 3.