Existence of the solutions of eliptic equations with nonstandard growth condition via variational approach

In the first chapter, the necessary knowledge about development of the space and literature are given.In the second chapter, some basic definitions and theorems are given which are the necessary for properly understanding of the following chapters. Moreover, the Lebesgue and Sobolev space are mentioned.In the third chapter, variational approach and the related basic concepts, definitions and theorems are given. Furthermore, applications of variational approach to the some problem types are given.In the fourth chapter, in view of variational approach, by using Mountain Pass Theorem and Cerami condition the the existence of nontrivial solutions of an elliptic system are obtained.In the fifth chapter, in view of variational approach, by using Krasnoselskii?s Genus Theorem and Palais-Smale condition the the existence of nontrivial solutions of a Kirchhoff equation are obtained.