On the difference equation zm+1 = f(zm, zm-1, …, zm–k)
نویسندگان
چکیده
منابع مشابه
On the nature of solutions of the difference equation $mathbf{x_{n+1}=x_{n}x_{n-3}-1}$
We investigate the long-term behavior of solutions of the difference equation[ x_{n+1}=x_{n}x_{n-3}-1 ,, n=0 ,, 1 ,, ldots ,, ]noindent where the initial conditions $x_{-3} ,, x_{-2} ,, x_{-1} ,, x_{0}$ are real numbers. In particular, we look at the periodicity and asymptotic periodicity of solutions, as well as the existence of unbounded solutions.
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and Applied Analysis 3 From 2.3 we obtain c 1 b b 1 2b 1 b 1 ⇒ b 1 b 1 2b 1 3b 2 2b 1 , 2.4 which implies b2 − b − 1 0. Hence b x1 or b x2. From this and 2.3 it follows that a b c x1 or a b c x2, from which the result follows. Theorem 2.3. Equation 1.1 has no prime period-four solutions. Proof. Let xn n −2 be a prime period-four solution of 1.1 and x−2 a, x−1 b, x0 c. Then we have x1 x0x−2 − 1 ...
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ژورنال
عنوان ژورنال: Journal of Taibah University for Science
سال: 2019
ISSN: 1658-3655
DOI: 10.1080/16583655.2019.1678866