Inverse Equivalent Points Problem Of Regular Sturm-Liouville Operator

The inverse equivalent points problem of regular Sturm-Liouville operator is mainly concerned with the uniqueness and reconstruction of the system by using equivalent points of eigenfunctions.The application of this problem is not only important in mathematics but also has a wide and direct application in physics and natural science.Therefore,the inverse equivalent points problem of this system has gotten more and more attention and been talked about by mathematician and physical and become one of the popular researches in applied mathematics.In this paper,we consider regular Sturm-Liouville system.The main works are given as follows:In the first chapter,we summarize the research backgrounds,significance and development of the inverse Sturm-Liouville operator,point out that the inverse equivalent points problem is the promotion of inverse nodal problem and briefly introduce the main work of this paper.In the second chapter,we consider the inverse equivalent points problem for the Neumann-Dirichlet boundary conditions,and give the proof of the uniqueness and the reconstruction of potential function.In the third chapter,we consider the inverse equivalent points problem for the Dirichlet-Dirichlet boundary conditions.If we are given the equivalent points of the derivative of eigenfunctions,then we can uniquely determine and reconstruct potential function.