Solution of nonlinear difference equations with the inverse operator

From the expression ∆f(x)=g(x) where ∆ is the forward difference, the f(x) function can be determined as f(x)=∆^(-1) g(x) Likewise, fort he equaiton ∆y(x)=p(x), where y(x) is an unknown function, the unknown function y(x) can be determined as y(x)=∆^(-1) p(x). In this study, using the ∆^(-1) operator, the general solutions of some linear or non-linear difference equations are expressed as theorems and explained with examples. With the help of this study, general solutions can be obtained for many more linear or non-linear difference equations. In the first part of the thesis, it is stated how far sicentists have progressed from the past to the present about the difference equations. The second part includes the discrete points set and fragmentation functions. In iddition, operators that help in solving difference equations and their features, solution and classification of difference equations are emphasized. It is explained how these operators work with examples. In the third part of the thesis, the classification of difference equations, basic concepts, the definition, the order, the difference equations from the n. order, general and specific solution, linearity solutions are emphasized. In the fourth part, some difference equations is proven by theorems that are linear (homogeneous and non-homogeneous) and non-lineer with the help of the inverse difference operator and explained with examples. And finally, other conclusions and recommendations are mentioned in the lost part of the thesis.