Báo cáo hoa học: " Research Article Convergence Results on a Second-Order Rational Difference Equation with Quadratic Terms"

Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article Convergence Results on a Second-Order Rational Difference Equation with Quadratic Terms | Hindawi Publishing Corporation Advances in Difference Equations Volume 2009 Article ID 985161 7 pages doi 2009 985161 Research Article Convergence Results on a Second-Order Rational Difference Equation with Quadratic Terms D. M. Chan C. M. Kent and N. L. Ortiz-Robinson Department of Mathematics and Applied Mathematics Virginia Commonwealth University Harris Hall 1o15 Floyd Avenue . Box 842014 Richmond VA 23284-2014 USA Correspondence should be addressed to C. M. Kent cmkent@ Received 6 March 2009 Accepted 20 June 2009 Recommended by Martin J. Bohner We investigate the global behavior of the second-order difference equation xn 1 xn-1 axn Pxn-1 Axn Bxn-1 where initial conditions and all coefficients are positive. We find conditions on A B a p 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. Copyright 2009 D. M. Chan et al. This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited. 1. Introduction and Preliminaries There are a number of studies published on second-order rational difference equations see . 1-9 . We investigate the global behavior of the second-order difference equation _ axn pxn-1 xn 1 _ xn-1 A D Axn Bxn-1 where the numerator is quadratic and the denominator is linear with A B a p e 0 to . Under various hypotheses on the parameters we establish the existence of different behaviors of even and odd subsequences of solutions of . Our results are summarized below. i Let a A and p B then we have the following. a There are infinitely many .

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