SOLVABILITY OF NONLINEAR DIFFERENCE EQUATIONS OF FOURTH ORDER

In this article we show the existence of solutions to the nonlinear difference equation x(n) = x(n-3)x(n-4)/x(n-1)(a(n) + b(n)x(n-2)x(n-3)x(n-4)), n is an element of N-0, where the sequences (a(n))(n is an element of N0) and (b(n))(n is an element of N0), and initial the values x(-j), j = (1, 4) over bar, are real numbers. Also we find the set of initial values for which solutions are undefinable when a(n) not equal 0 and b(n) not equal 0 for every n is an element of N-0. When these two sequences are constant, we describe the long-term behavior of the solutions in detail.