General solutions to four classes of nonlinear difference equations and some of their representations

Abstract

We present general solutions to four classes of nonlinear difference equations, as well as some representations of the general solutions for two of the classes in terms of specially chosen solutions to linear homogeneous difference equations with constant coefficients which are naturally associated to the equations of the classes. Our main results considerably generalize some very special ones in recent literature, and present concrete methods for solving the equations.

Keywords

• difference equation
• solvable difference equation
• representation of general solutio