RATIONAL DIFFERENCE EQUATIONS WITH POSITIVE EQUILIBRIUM POINT
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In this note we study positive solutions of the mth order rational difference equation xn = (a0 +∑m i=1 aixn−i)/(b0 +∑m i=1 bixn−i),where n = m,m+1,m+2, . . . and x0, . . . , xm−1 > 0. We describe a sufficient condition on nonnegative real numbers a0, a1, . . . , am, b0, b1, . . . , bm under which every solution xn of the above equation tends to the limit (A − b0 +p(A − b0)2 + 4a0B)/2B as n ! 1, where A =∑m i=1 ai and B =∑m i=1 bi.
Abstract
In this note we study positive solutions of the mth order rational difference equation xn = (a0 +∑m i=1 aixn−i)/(b0 +∑m i=1 bixn−i),where n = m,m+1,m+2, . . . and x0, . . . , xm−1 > 0. We describe a sufficient condition on nonnegative real numbers a0, a1, . . . , am, b0, b1, . . . , bm under which every solution xn of the above equation tends to the limit (A − b0 +p(A − b0)2 + 4a0B)/2B as n ! 1, where A =∑m i=1 ai and B =∑m i=1 bi.
참고문헌 (4)
- E. Camouzis, "Global analysis of solutions of xn+1 = βxn+±δxn−2", A+Bxn+Cxn−1, 2006, pp.316(2), 616~627
- E. Camouzis, "Dynamics of Third-Order Rational Difference Equations withOpen Problems and Conjectures, Advances in Discrete Mathematics and Applications, 5", pp.2008, Chapman & Hall
- M. R. S. Kulenović, "Dynamics of Second Order Rational Difference Equations, With open problems and conjectures", pp.2002, Chapman & Hall
- "대한수학회논문집", 2008, 61~65, pp.대한수학회