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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.
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참고문헌 (4)
참고문헌 신청
E. Camouzis / 2006 / Global analysis of solutions of xn+1 = βxn+±δxn?2/A+Bxn+Cxn?1 / J. Math. Anal. Appl. 316 (2) : 616 ~ 627
E. Camouzis / 2008 / Dynamics of Third-Order Rational Difference Equations withOpen Problems and Conjectures, Advances in Discrete Mathematics and Applications, 5 / Chapman & Hall/CR
M. R. S. Kulenovi? / 2002 / Dynamics of Second Order Rational Difference Equations, With open problems and conjectures / Chapman & Hall/CRC
박종안 / 2008 / A global behavior of the positive solutions of [수식] / 대한수학회논문집 23 (1) : 61 ~ 65
E. Camouzis / 2008 / Dynamics of Third-Order Rational Difference Equations withOpen Problems and Conjectures, Advances in Discrete Mathematics and Applications, 5 / Chapman & Hall/CR
M. R. S. Kulenovi? / 2002 / Dynamics of Second Order Rational Difference Equations, With open problems and conjectures / Chapman & Hall/CRC
박종안 / 2008 / A global behavior of the positive solutions of [수식] / 대한수학회논문집 23 (1) : 61 ~ 65
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