On the difference equationx_{n + 1} = \frac{{a + bx_{n - k} - cx_{n - m} }}{{1 + g(x_{n - 1} )}} |
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Authors: | Guang Zhang Stevo Stević |
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Institution: | 1. School of Science, Tianjin University of Commerce, 300134, Tianjin, P. R. China 2. Mathematical Institute of the Serbian Academy of Science, 11000, Knez Mihailova 35/I, Beograd
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Abstract: | In this paper we consider the difference equation $$x_{n + 1} = \frac{{a + bx_{n - k} - cx_{n - m} }}{{1 + g(x_{n - 1} )}},$$ wherea, b, c are nonegative real numbers,k, l, m are nonnegative integers andg(x) is a nonegative real function. The oscillatory and periodic character, the boundedness and the stability of positive solutions of the equation is investigated. The existence and nonexistence of two-period positive solutions are investigated in details. In the last section of the paper we consider a generalization of the equation. |
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