A general fourth-order regular ordinary differential equation with eigenvalue dependent boundary conditions and transmission conditions are considered. We prove that the eigenvalues depend continuously and smoothly on the coefficients of the differential equation and on the boundary and transmission matrices. We provide as well formulas for the derivatives with respect to each of these parameters.
"Dependence of eigenvalues of fourth-order boundary value problems with transmission conditions." Rocky Mountain J. Math. 50 (1) 369 - 381, Febuary 2020. https://doi.org/10.1216/rmj.2020.50.369