The soluation of Dirichlet problem for p(x) Laplacian involving gradient via Mountain Pass and iteration techniques

The first chapter of this thesis presents an overview about physical applications of non-standart growth conditions in differential equations and the historical development of variable exponent Lebesgue, Sobolev spaces. Moreover, a brief information are given about the studies of the related non-standart growth conditions differential equations. The second chapter introduces the basic definitions and theorems as well as Lebesgue and Sobolev spaces which are related to the work done in this thesis. In the third part, the variational approach and basic definitions and theorems related to this approach and the methods used in the variational approach are introduced. In the fourth chapter, the solution of the Dirichlet problem for the p(x)-Laplacian equation involving Gradient is given using Mountain Pass