Investigation of impulsive dirac equations

This thesis consists of five chapters. The first chapter is devoted to the introduction. In the second chapter, some well known concepts of functional analysis and spectral theory are mentioned and an example of an eigenvalue problem is presented. In the third chapter, the matrix equation \begin{equation*} K\dfrac{d\psi}{dx}+P(x)\psi=\mu\psi,\quad \psi(x)=\begin{pmatrix} \psi_{1}(x)\\ \psi_{2}(x) \end{pmatrix},\quad x\in[0,\pi] \end{equation*} is introduced, where µ is a spectral parameter, $ K=\begin{pmatrix} 0&1\\ -1&0 \end{pmatrix}$, \: $ P=\begin{pmatrix} P_{11}&P_{12}\\ P_{21}&P_{22} \end{pmatrix}$ and $ P_{ij} $ \: are real valued functions which are continuous on the interval $[0,\pi] $ for $ i,j=1,2. $ The fourth chapter consists of two sections. In the first section, the impulsive Dirac operator is defined, theory on the eigenvalues and the spectral singularities of this operator is given. In the second section, some special cases are examined, where the impulsive condition at the origin has certain symmetries. The fifth and last chapter is devoted to the conclusion and recommendations.