A Prüfer Angle Approach to Dependence of Eigenvalue for Sturm‐Liouville Problem With Distributional Potentials

In this paper, we apply the Prüfer transformation to investigate the dependence of eigenvalues for the Sturm–Liouville problem with distributional potentials. Based on several important properties of Prüfer angle established herein, the precise oscillation theorems for the problem are obtained. Moreover, it is proved that the eigenvalue functionals are not only completely continuous but also continuously differentiable in potentials. Meanwhile, we derive the precise Fréchet derivative formula of eigenvalue in potentials.