Inverse Problem for the Quadratic Pencil of the Sturm-Liouville Equations

Abstract

In this paper, we study the wellposedness of the inverse problem for the quadratic pencil of the Sturm-Liouville equation (diffusion operator). We will consider two different problem for diffusion operator. By using the Mizutani's method, we will prove that if the spectral characteristics of this problems are close to each other, then the difference between their potential functions is sufficiently small in a certain sense.