Abstract
Closed form formulas for well-defined solutions of the next difference equation
x(n) = x(n-2)x(n-k-2) / x(n-k)(a(n) + b(n)x(n-2)x(n-k-2)); n is an element of N-0;
where k is an element of N, (a(n))(n is an element of N0); ((b)n)(n) (is an element of N0); and initial values x(-i), i = 1; (k + 2) over bar are real numbers, are given. Long-term behavior of well-defined solutions of the equation when (a(n))(n is an element of N0) and (b(n))(n is an element of N0) are constant sequences is described in detail by using the formulas. We also describe the domain of undefinable solutions of the equation. Our results explain and considerably improve some recent results in the literature.