Perturbation theory in elliptic equations

In this thesis, the methods used in perturbation theory to find the approximate series solution in elliptic partial differential equations and their various uses are introduced. The applications of these methods to elliptic problems are given. This thesis work consists of six chapters: In the first chapter, a summary of the literature on the subject is given. In the second chapter, some basic concepts used throughout the thesis are expressed. In the third chapter, asymptotic order symbols and asymptotic approximations are introduced. Perturbation theory is mentioned, and also uniform and singular perturbation applications are covered. In the fourth and fifth chapters, homotopy perturbation and homotopy perturbation transform methods are introduced and applications are given. In the sixth chapter, the results are given.