Inverse Sturm-Liouville Problems with Self-Adjoint Non-Separated Boundary Conditions

The present monograph provides the first systematic analysis of inverse Sturm-Liouville problems with self-adjoint non-separated boundary conditions. The work summarizes and complements the results, which the author obtained and published in journal articles.

The book consists of three chapters. The first chapter proves the earliest theorems on the uniqueness of solutions of inverse Sturm-Liouville problems with self-adjoint non-separated boundary conditions; to prove their point the authors used the method of mapping of solution spaces. The second chapter presents the author’s theorems on the uniqueness, solvability and stability of solutions for the Sturm-Liouville problem with self-adjoint non-separated boundary conditions, and a pencil of differential operators. Appropriate examples and counterexamples are also given. In contrast to the first part, the basic method for solving inverse problems is the one of auxiliary problems rather than one of mapping solution spaces. The third chapter presents the results of reconstructing the boundary conditions for the Sturm-Liouville problem with the known differential equation.