A class of nonlocal elliptic equations in Orlicz-sobolev spaces

In the first chapter, the basic concepts related to the subject, notations, theorems and lebesque and sobolev spaces related to the topics to be studied are given. In the second chapter, Orlicz spaces and Orlicz-sobolev spaces and basic concepts, notation and theorems related to these spaces are discussed. In the third chapter, we investigate the variational approach. Definitions and theorems related to the variational approach are given. The variational approach is a method used in the analysis of the problem that is the subject of this thesis. The fourth chapter contains the orginal part of this thesis. In this chapter, we consider solutions of some classes of a nonlocal eliptic equation under the Dirichlet boundry conditions and in OrliczSobolev spaces. Applying the variational appoach to this equation gives trivial solutions, which are local minimum, for the corresponding energy functional.