Solvable subclasses of a class of nonlinear second-order difference equations

Abstract

We present some solvable subclasses of the class of nonlinear second-order difference equations of the form Axn+1 + Bxn+1xn + Cxnxn-1 + Gxn+1xn-1 + Dxn + Exn-1 + F = 0, n ∈ ℕ0, where the parameters A, B, C, D, E, F, G and the initial values x-1,x0 are real numbers. This difference equation is a natural extension of the nonhomogeneous linear second-order difference equation with constant coefficients as well as of the bilinear difference equation with constant coefficients.

Keywords

• second-order difference equation
• nonlinear solvable difference equation
• closed form solution
• 39a10
• 39a20