Dependence of Eigenvalues of Discontinuous Fourth-order Differential Operators with Eigenparameter Dependent Boundary Conditions

In this paper, we investigate a fourth-order differential operator with eigenparameter dependent boundary conditions and transmission conditions. To study the eigenvalues of the problem, we establish a new operator associated with the considered problem. Furthermore, we prove that the eigenvalues are differentiable depending on the parameters of the problem. Finally, the differential expressions of the eigenvalues with respect to all parameters are given.