Derivatives of Eigenvalues of Third-Order Problems

Abstract

In this chapter, we aim to introduce some properties of the eigenvalues of some third-order boundary-value-transmission problems generated by the following differential expression where the coefficients are real-valued and Lebesgue measurable functions on a given interval. In particular, we aim to show that the eigenvalues of the problems are differentiable with respect to some elements of data. Moreover, we will share some ordinary and Frechet derivatives of the eigenvalues with respect to some elements of data. Note that the results are new in the literature. However, the readers may find some results for the special case s = 0 in the literature. © 2020 Nova Science Publishers, Inc.