Localization and perturbation of complex zeros of solutions to second order differential equations with polynomial coefficients. A survey
In the main results of this paper the author derives estimates for the sums and products of the zeros of solutions to linear homogeneous second order ordinary differential equations with polynomial coefficients. These estimates are bounds for the function counting the zeros of solutions and information about the zero-free domain. Some other applications of the obtained estimates for the sums and products of the zeros are also discussed. In addition, the author investigates the variation of the zeros of solutions under perturbations of the coefficients. Illustrative examples are also presented. This paper is a survey of the recent results of the author on the complex zeros of solutions to linear homogeneous second order ordinary differential equations with polynomial coefficients, and presents some new results. It is of great significance for future research. For the entire collection see [Zbl 1471.34005].
linear differential equation in complex plane
scientific article; zbMATH DE number 7392143
scientific article