Generic simplicity of the eigenvalues for a supported plate equation

In this work, we show that the eigenvalues of the problem {(Δ2+V(x)+λ)u(x)=0x∈Ωu(x)=Δu(x)=0x∈∂Ω are generically simple in the set of C4C4 regular regions of RnRn, n≥2n≥2. In fact, we prove that there exists a residual set of regions C4C4 diffeomorphic to a given ΩΩ such that all the eigenvalues for a supported plate equation are simple.