Characteristic polynomials and asymptotic expressions for solutions of a boundary value problem with two interval

This thesis is carried out to investigate asymptotic expressions of a two interval boundary value problem and the characteristic (quasi) polynomials belong to the eigenvalues of the problem. This thesis is essentially consists of eight chapters. In the first chapter some informations about the subject of the thesis are given. In the second chapter, some fundamental definitions and properties about differential equations, some spaces and linear operators are given. In the third chapter, the definition of the big-O and the small-o notations which are the asymptotic notitions are defined. In addition to these definitions some theorems and examples about the big-O and the small-o notations are given. In the fourth chapter, some fundamental definitions, theorems and examples about matrices and system of linear equations are given. Furthermore the terms distinct eigenvalue, repeated eigenvalue, defective eigenvalue and non-defective eigenvalue are introduced. These terms are examined with details. In addition to these, in this chapter, the expressions generalized eigenvalue, algebraic power, geometric power, eigenspace and eigenbasis are introduced. In the fifith chapter, the differential operator, boundary value problem and the Sturm Liouville boundary value problem are introduced. Moreover in this chapter, eigenvalue and eigenfunction problems which are belong to boundary value problem and Sturm Liouville boundary value problem are examined. In the sixth chapter, asymptotic expressions about a two interval boundary value problem and the characteristic (quasi) polynomials belong to the eigenvalues of this problem are given. In the seventh chapter, the materials and the methods that we used in our thesis are explained. In the eighth chapter, conclusions and recommendations related with this thesis are given.