Abstract
This paper shows that all positive solutions of a higher‐order nonlinear difference equation are bounded, extending some recent results in the literature.
Highlights
There is a considerable interest in studying nonlinear difference equations nowadays; see, for example, 1–40 and numerous references listed therein.The investigation of the higher-order nonlinear difference equation xn A xnp−m xnr −k, n ∈ N0, 1.1 where A, r > 0 and p ≥ 0, and k, m ∈ N, k / m, was suggested by Stevicat numerous talks and in papers see, e.g., 20, 28, 30, 34–38 and the related references therein .In this paper we show that under some conditions on parameters A, r, and p all positive solutions of the difference equation xn xnp−1 xnr −k1.2 where k ∈ N \ {1}, are bounded
We investigate the boundedness of the positive solutions to 1.2 for the case 0 < p < rkk/ k − 1 k−1 1/k
“On the recursive sequence xn 1 α − xn/xn−1 ,” Journal of Applied Mathematics & Computing, vol 17, no. 1-2, pp. 269–282, 2005
Summary
There is a considerable interest in studying nonlinear difference equations nowadays; see, for example, 1–40 and numerous references listed therein. N ∈ N0, 1.1 where A, r > 0 and p ≥ 0, and k, m ∈ N, k / m, was suggested by Stevicat numerous talks and in papers see, e.g., 20, 28, 30, 34–38 and the related references therein. In this paper we show that under some conditions on parameters A, r, and p all positive solutions of the difference equation xn xnp−1 xnr −k. 1.2 where k ∈ N \ {1}, are bounded. To do this we modify some methods and ideas from Stevic’s papers 30, 35–37. Our motivation stems from these four papers
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