Research On Characterization Of Some Differential Operators

differential operators: spectral analysis. First we analyze the eigenvalues of a class of Sturm-Liouville problems of 4-order, then we conclud that the eigenvalues are continuous and differentiable functions of all the data:the endpoints,the boundary conditions,the coefficients and the weight function,and we find expressions for their derivatives.Then we consider the eigenvalues of a class of Sturm-Liouville problems of 2n-order, then we conclud that the eigenvalues are continuous and differentiable functions of all the data:the endpoints,the boundary conditions,the coefficients and the weight function,and we find expressions for their derivatives.This paper contains three parts. The first part: an introduction of the background of the problems we investigate and main results we obtain in this paper. The second part: we consider the continuity and differentiability of the eigenvalues of a class of Sturm-Liouville problems of 4-order. The third part: we consider the continuity and differentiability of the eigenvalues of a class of Sturm-Liouville problems of 2n-order.