Asymptotic behavior of eigenvalues of fourth-order differential operators with spectral parameter in the boundary conditions

We consider a spectral problem for a fourth-order differential equation with spectral parameter dependent boundary conditions. We determine the high energy eigenvalue behavior for this operator. Moreover, if the coefficient of differential equation is sufficiently smooth, we can obtain sharp eigenvalue asymptotic behavior. This behavior exhibits a non-standard high-frequency effect generated by the spectral parameter in the boundary conditions. For more information see https://ejde.math.txstate.edu/Volumes/2024/62/abstr.html