A GLOBAL BEHAVIOR OF THE POSITIVE SOLUTIONS OF xn+1=βxn+ xn-2⁄ A+Bxn+ xn-2
نویسندگان
چکیده
منابع مشابه
The behaviour of the positive solutions of the difference equation xn 5 A 1 xn 2 2 xn 2 1 p
xn 1⁄4 Aþ xn22 xn21 p ; n 1⁄4 0; 1; . . .; with p, A [ (0, 1), p – 1 and x22, x21 [ (0, 1). It is shown that: (a) all solutions converge to the unique equilibrium, x 1⁄4 Aþ 1, whenever p # min{1, (A þ 1)/2}; (b) all solutions converge to period two solutions whenever (A þ 1)/2 , p , 1; and (c) there exist unbounded solutions whenever p . 1. These results complement those for the case p 1⁄4 1 in...
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متن کاملON BOUNDEDNESS OF THE SOLUTIONS OF THE DIFFERENCE EQUATION xn+1=xn-1/(p+xn)
Theorem 1. (i) If p > 1, then the unique equilibrium 0 of (1) is globally asymptotically stable. (ii) If p = 1, then every positive solution of (1) converges to a period-two solution. (iii) If 0 < p < 1, then 0 and x = 1− p are the only equilibrium points of (1), and every positive solution {xn}n=−1 of (1) with (xN − x)(xN+1 − x) < 0 for some N ≥ −1 is unbounded. They proposed the following ope...
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ژورنال
عنوان ژورنال: Communications of the Korean Mathematical Society
سال: 2008
ISSN: 1225-1763
DOI: 10.4134/ckms.2008.23.1.061