On solutions of nonlocal equations in Orlicz-Sobolev spaces

In the first chapter, the basic concepts, notation and theorems regarding Lebesgue and Sobolev spaces are given. In the second section, the basic concepts, notation and theorems regarding Orlicz spaces are given. In the third section, the basic concepts,notation and theorems of the variational approach and are given. The variational approach has been applied to many problem types since it is a very effective tool for analyzing nonlinear partial differential equations. The absence of a general theory that solves every type of nonlinear differential equations has increased the importance of the variational approach. In short, the variational approach is a method that aims to find the solution of the given differential equation by corresponding its solutions to the critical points of the corresponding energy functional or the minimize sequence instead of directly solving the differential equation. The fourth section is the original part of the thesis work, in which the solutions of a nonlocal elliptic equation with Robin boundary-value conditions are obtained in Orlicz-Sobolev spaces by using the variational approach and the Ekeland variational principle.