On a solvable class of nonlinear difference equations of fourth order

Abstract

We consider a class of nonlinear difference equations of the fourth order, which extends some equations in the literature. It is shown that the class of equations is solvable in closed form explaining theoretically, among other things, solvability of some previously considered very special cases. We also present some applications of the main theorem through two examples, which show that some results in the literature are not correct.

Keywords

• nonlinear difference equation
• solvable difference equation
• general solution
• closed-form formula for solutions