The solutions of difference equations at elliptic type involving nonstandard growth condition

In the first chapter, the necessary knowledge about development of the space and literature aregiven.In the second chapter, some basic definitions and theorems are given which are the necessaryfor properly understanding of the following chapters. Moreover, the Lebesgue and Sobolevspace are mentioned.In the third chapter, variational approach and the related basic concepts, definitions andtheorems are given. Furthermore, applications of variational approach to the some problemtypes are given.In the fourth chapter, by examining an elliptic equation involoving a discrete p ? k ? -Laplacianoperator, at least three non-zero solutios are shown with Ricceri?s three critical pointstheorem.In the fifth chapter, by examining via variational approach discrete problem at Kirchhoff type,