Positive solutions of functional difference equations with -Laplacian operator.

Song, Chang-Xiu

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Existence of positive solutions for boundary value problems of nonlinear functional difference equation with $p$ -Laplacian operator.

Yang, S.J., Shi, B., Zhang, D.C. (2007)

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On the behavior of solutions of the system of rational difference equations: $x_{n + 1} = x_{n - 1} / (y_{n} x_{n - 1} - 1)$ , $y_{n + 1} = y_{n - 1} / (x_{n} y_{n - 1} - 1)$ , and $z_{n + 1} = z_{n - 1} / (y_{n} z_{n - 1} - 1)$ .

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On the solutions of the system of difference equations $x_{n + 1} = max {A / x_{n}, y_{n} / x_{n}}$ , $y_{n + 1} = max {A / y_{n}, x_{n} / y_{n}}$ .

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Existence criteria and classification schemes for positive solutions of second-order nonlinear difference systems.

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Oscillatory criteria for the two-dimensional difference systems.

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On the system of rational difference equations $x_{n + 1} = f (x_{n}, y_{n - k})$ , $y_{n + 1} = f (y_{n}, x_{n - k})$ .

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On the system of rational difference equations $x_{n + 1} = f (y_{n - q}, x_{n - s})$ , $y_{n + 1} = g (x_{n - t}, y_{n - p})$ .

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On a max-type difference equation.

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Some boundedness results for systems of two rational difference equations

Gabriel Lugo, Frank Palladino (2010)

Open Mathematics

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We study k th order systems of two rational difference equations $x_{n} = \frac{α + \sum_{i = 1}^{k} β_{i} x_{n - 1} + \sum_{i = 1}^{k} γ_{i} y_{n - 1}}{A + \sum_{j = 1}^{k} B_{j} x_{n - j} + \sum_{j = 1}^{k} C_{j} y_{n - j}}, y_{n} = \frac{p + \sum_{i = 1}^{k} δ_{i} x_{n - i} + \sum_{i = 1}^{k} ε_{i} y_{n - i}}{q + \sum_{j = 1}^{k} D_{j} x_{n - j} + \sum_{j = 1}^{k} E_{j} y_{n - j}} n \in ℕ$ . In particular, we assume non-negative parameters and non-negative initial conditions, such that the denominators are nonzero. We develop several approaches which allow us to extend well known boundedness results on the k th order rational difference equation to the setting of systems in certain cases.

On the stability of trigonometric functional equations.

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Displaying similar documents to “Positive solutions of functional difference equations with p -Laplacian operator.”

Displaying similar documents to “Positive solutions of functional difference equations with $p$ -Laplacian operator.”