Block-radial symmetry breaking for ground states of biharmonic NLS

We prove that the biharmonic NLS equation Delta(2)u + 2Au + (1 + epsilon)u = |u|(p-2)u in R-d has at least k+1 geometrically distinct solutions if epsilon>0 is small enough and 2<p<2(star)(k), where 2(star)(k) is an explicit critical exponent arising from the Fourier restriction theory of o(d-k)xo(k)-symmetric functions. This extends the recent symmetry breaking result of Lenzmann-Weth (Symmetry breaking for ground states of biharmonic NLS via Fourier extension estimates, 2023) and relies on a chain of strict inequalities for the corresponding Rayleigh quotients associated with distinct values of k. We further prove that, as epsilon -> 0+, the Fourier transform of each ground state concentrates near the unit sphere and becomes rough in the scale of Sobolev spaces.