Dependence of Eigenvalues of $$(2n + 1)$$ th Order Boundary Value Problems with Transmission Conditions

Abstract

This paper deals with some boundary value problems generated by $$(2n + 1)$$ ( 2 n + 1 ) th order differential equation with transmission conditions. After showing that these problems generate self-adjoint operators and the eigenvalues of the problems are real, we introduce the continuous dependence and differentiable dependence of eigenvalues on parameters: coefficient functions and weight function, boundary conditions, transmission conditions, as well as the endpoints and transmission points. In addition, we obtain the differential expressions of all given parameters respectively.