Convergence Results on a Second-Order Rational Difference Equation with Quadratic Terms. (19th July 2009)

• Record Type: Journal Article
• Authors: Chan, D. M.; Kent, C. M.; Ortiz-Robinson, N. L.
• Other Names: Bohner Martin J. Academic Editor.
• Is Part Of: Advances in difference equations. Volume 2009(2009)
• Publication Date: 2009-07-19
• Subjects: Difference equations -- Periodicals; 515.625
• DOI: 10.1155/2009/985161
• Languages: English
• ISSNs: 1687-1847

Abstract

Abstract : We investigate the global behavior of the second-order difference equationx n + 1 = x n − 1 ( α x n + β x n − 1 )/( A x n + B x n − 1 ), where initial conditions and all coefficients are positive. We find conditions onA, B, α, β under which the even and odd subsequences of a positive solution converge, one to zero and the other to a nonnegative number; as well as conditions where one of the subsequences diverges to infinity and the other either converges to a positive number or diverges to infinity. We also find initial conditions where the solution monotonically converges to zero and where it diverges to infinity.