Some properties and expressions of solutions for a class of nonlinear difference equation (Q2895404)

The authors study properties of solutions of the following second order difference equation NEWLINE\[NEWLINE x_{n+1}=ax_{n-2}+\frac{bx_{n-2}x_{n-3}}{cx_n+dx_{n-3}}, \;\;n=0,1,\dots, NEWLINE\]NEWLINE where \(a\), \(b\), \(c\), \(d\) are constants, with positive initial values \(x_{-3}\), \(x_{-2}\), \(x_{-1}\), \(x_{0}\). If \((c+d)(1-a)\neq b\), this equation has a unique equilibrium point \(x=0\). Local and global stability of the equilibrium point and boundedness of solutions are investigated. The expressions for solutions are derived in some special cases.