Solvability and representations of the general solutions to some nonlinear difference equations of second order

We give detailed theoretical explanations for getting the closed-form formulas and representations for the general solutions to four special cases of a class of nonlinear difference equations of second order considered in the literature, present an extension of the class of difference equations which is solvable in closed form, analyze some results on the long-term behavior of the solutions to the class of equations, and give some results on convergence.

Automated summary

We provide theoretical explanations for obtaining closed-form formulas and representations of general solutions for four special cases of a class of nonlinear second-order difference equations. We also propose an extension of this class of equations that can be solved in closed form, analyze the long-term behavior of the solutions, and present some convergence results.