Determination of first order perturbation for bi-harmonic operator by asymptotic boundary spectral data

This article deals with the multidimensional Borg-Levinson theorem for perturbed bi-harmonic operator. More precisely, in a bounded smooth domain of ${\mathbb{R}}^n$, with $n\ge 2$, we prove the stability of the first and zero order coefficients of the bi-harmonic operator from some asymptotic behavior of the boundary spectral data of the corresponding bi-harmonic operator i.e., the Dirichlet eigenvalues and the Neumann trace on the boundary of the associated eigenfunctions.