Tollu, Durhasan TurgutYazlik, YasinTaskara, Necati2024-02-232024-02-2320181300-00981303-6149https://doi.org/10.3906/mat-1705-33https://hdl.handle.net/20.500.12452/16065In this paper we consider the following higher-order nonlinear difference equation x(n) = alpha x(n-k) + delta x(n-k)x(n-(k+l))/beta x(n-(k+l)) + gamma x(n-1), n is an element of N-0, where k and l are fixed natural numbers, and the parameters alpha, beta, gamma, delta and the initial values x(-i), i = (1, k +l) over bar, are real numbers such that beta(2) + gamma(2) not equal 0. We solve the above-mentioned equation in closed form and considerably extend some results in the literature. We also determine the asymptotic behavior of solutions and the forbidden set of the initial values using the obtained formulae for the case l = 1.eninfo:eu-repo/semantics/openAccessDifference EquationsSolution In Closed FormForbidden SetAsymptotic BehaviorArticle424176517782-s2.0-85050724550Q2WOS:000439579600017Q310.3906/mat-1705-33