The Speed Of Sound With A Spherically Symmetric Transmission Characteristics Value Problem

It’s well known that Sturm-Liouville theory has been used in physics, engineer-ing and technology and other types applied subject. Many scientists carried out in-depth study of the theory. This article mainly dicusses the problem of a spheri-cally symmetric speed sound of interior transmission eigenvalues. It is transformed into a Sturm-Liouville problem from interior transmission eigenvalues by using Li-ouville transform. Then the uniqueness and the eigenvalues of asymptotic formula is considered and the associated spectral information is used to obtain the trace formula accordingly.The contents of this paper is arranged as follows:Chapter1the background of the problem and main content of this paper are introduced.Chapter2the uniqueness result for the inverse problem of a Schrodinger op-erator is studied. The potential function is uniquely determined by the eigenvalues including their multiplicities and a related parameter in certain conditions based on the knowledge of inverse spectral theory for Sturm-Liouville problems.Chapter3the spectral information of a nonselfadjoint Sturm-Liouville equation in the right boundary conditions is considered. It obtains that asymptotic expres-sions of the real eigenvalues and the trace formula with the knowledge of spectral theory and the properties of entire function.Chapter4the eigenvalue problems of a Sturm-Liouville equation with parame-ter h, H and spectral parameter A in the boundary conditions is discussed. It obtains that asymptotic expressions of the real eigenvalue on the based of a more general boundary conditions.